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No. FEDERALIST 10
The Same Subject Continued(The Union as a Safeguard Against
Domestic Faction and Insurrection) From the New York Packet.Friday,
November 23, 1787.James Madison
To the People of the State of New York:
AMONG the numerous advantages promised by a wellconstructed Union,
none deserves to be more accurately developed than its tendency to break
and control the violence of faction. The friend of popular governments
never finds himself so much alarmed for their character and fate, as when
he contemplates their propensity to this dangerous vice. He will not fail,
therefore, to set a due value on any plan which, without violating the
principles to which he is attached, provides a proper cure for it. The
instability, injustice, and confusion introduced into the public councils,
have, in truth, been the mortal diseases under which popular governments
have everywhere perished; as they continue to be the favorite and fruitful
topics from which the adversaries to liberty derive their most specious
declamations. The valuable improvements made by the American
constitutions on the popular models, both ancient and modern, cannot
certainly be too much admired; but it would be an unwarrantable partiality,
to contend that they have as effectually obviated the danger on this side,
as was wished and expected. Complaints are everywhere heard from our
most considerate and virtuous citizens, equally the friends of public and
private faith, and of public and personal liberty, that our governments are
too unstable, that the public good is disregarded in the conflicts of rival
parties, and that measures are too often decided, not according to the
rules of justice and the rights of the minor party, but by the superior force
of an interested and overbearing majority. However anxiously we may wish
that these complaints had no foundation, the evidence, of known facts will
not permit us to deny that they are in some degree true. It will be found,
indeed, on a candid review of our situation, that some of the distresses
under which we labor have been erroneously charged on the operation of
our governments; but it will be found, at the same time, that other causes
will not alone account for many of our heaviest misfortunes; and,
particularly, for that prevailing and increasing distrust of public
engagements, and alarm for private rights, which are echoed from one end
of the continent to the other. These must be chiefly, if not wholly, effects of
the unsteadiness and injustice with which a factious spirit has tainted our
public administrations.
By a faction, I understand a number of citizens, whether amounting to a
majority or a minority of the whole, who are united and actuated by some
common impulse of passion, or of interest, adversed to the rights of other
citizens, or to the permanent and aggregate interests of the community.
There are two methods of curing the mischiefs of faction: the one, by
removing its causes; the other, by controlling its effects.
There are again two methods of removing the causes of faction: the one,
by destroying the liberty which is essential to its existence; the other, by
giving to every citizen the same opinions, the same passions, and the
same interests.
It could never be more truly said than of the first remedy, that it was worse
than the disease. Liberty is to faction what air is to fire, an aliment without
which it instantly expires. But it could not be less folly to abolish liberty,
which is essential to political life, because it nourishes faction, than it would
be to wish the annihilation of air, which is essential to animal life, because
it imparts to fire its destructive agency.
The second expedient is as impracticable as the first would be unwise. As
long as the reason of man continues fallible, and he is at liberty to exercise
it, different opinions will be formed. As long as the connection subsists
between his reason and his self-love, his opinions and his passions will
have a reciprocal influence on each other; and the former will be objects to
which the latter will attach themselves. The diversity in the faculties of
men, from which the rights of property originate, is not less an insuperable
obstacle to a uniformity of interests. The protection of these faculties is the
first object of government. From the protection of different and unequal
faculties of acquiring property, the possession of different degrees and
kinds of property immediately results; and from the influence of these on
the sentiments and views of the respective proprietors, ensues a division
of the society into different interests and parties.
The latent causes of faction are thus sown in the nature of man; and we
see them everywhere brought into different degrees of activity, according
to the different circumstances of civil society. A zeal for different opinions
concerning religion, concerning government, and many other points, as
well of speculation as of practice; an attachment to different leaders
ambitiously contending for pre-eminence and power; or to persons of other
descriptions whose fortunes have been interesting to the human passions,
have, in turn, divided mankind into parties, inflamed them with mutual
animosity, and rendered them much more disposed to vex and oppress
each other than to co-operate for their common good. So strong is this
propensity of mankind to fall into mutual animosities, that where no
substantial occasion presents itself, the most frivolous and fanciful
distinctions have been sufficient to kindle their unfriendly passions and
excite their most violent conflicts. But the most common and durable
source of factions has been the various and unequal distribution of
property. Those who hold and those who are without property have ever
formed distinct interests in society. Those who are creditors, and those
who are debtors, fall under a like discrimination. A landed interest, a
manufacturing interest, a mercantile interest, a moneyed interest, with
many lesser interests, grow up of necessity in civilized nations, and divide
them into different classes, actuated by different sentiments and views.
The regulation of these various and interfering interests forms the principal
task of modern legislation, and involves the spirit of party and faction in the
necessary and ordinary operations of the government.
No man is allowed to be a judge in his own cause, because his interest
would certainly bias his judgment, and, not improbably, corrupt his
integrity. With equal, nay with greater reason, a body of men are unfit to be
both judges and parties at the same time; yet what are many of the most
important acts of legislation, but so many judicial determinations, not
indeed concerning the rights of single persons, but concerning the rights of
large bodies of citizens? And what are the different classes of legislators
but advocates and parties to the causes which they determine? Is a law
proposed concerning private debts? It is a question to which the creditors
are parties on one side and the debtors on the other. Justice ought to hold
the balance between them. Yet the parties are, and must be, themselves
the judges; and the most numerous party, or, in other words, the most
powerful faction must be expected to prevail. Shall domestic manufactures
be encouraged, and in what degree, by restrictions on foreign
manufactures? are questions which would be differently decided by the
landed and the manufacturing classes, and probably by neither with a sole
regard to justice and the public good. The apportionment of taxes on the
various descriptions of property is an act which seems to require the most
exact impartiality; yet there is, perhaps, no legislative act in which greater
opportunity and temptation are given to a predominant party to trample on
the rules of justice. Every shilling with which they overburden the inferior
number, is a shilling saved to their own pockets.
It is in vain to say that enlightened statesmen will be able to adjust these
clashing interests, and render them all subservient to the public good.
Enlightened statesmen will not always be at the helm. Nor, in many cases,
can such an adjustment be made at all without taking into view indirect and
remote considerations, which will rarely prevail over the immediate interest
which one party may find in disregarding the rights of another or the good
of the whole.
The inference to which we are brought is, that the CAUSES of faction
cannot be removed, and that relief is only to be sought in the means of
controlling its EFFECTS.
If a faction consists of less than a majority, relief is supplied by the
republican principle, which enables the majority to defeat its sinister views
by regular vote. It may clog the administration, it may convulse the society;
but it will be unable to execute and mask its violence under the forms of
the Constitution. When a majority is included in a faction, the form of
popular government, on the other hand, enables it to sacrifice to its ruling
passion or interest both the public good and the rights of other citizens. To
secure the public good and private rights against the danger of such a
faction, and at the same time to preserve the spirit and the form of popular
government, is then the great object to which our inquiries are directed. Let
me add that it is the great desideratum by which this form of government
can be rescued from the opprobrium under which it has so long labored,
and be recommended to the esteem and adoption of mankind.
By what means is this object attainable? Evidently by one of two only.
Either the existence of the same passion or interest in a majority at the
same time must be prevented, or the majority, having such coexistent
passion or interest, must be rendered, by their number and local situation,
unable to concert and carry into effect schemes of oppression. If the
impulse and the opportunity be suffered to coincide, we well know that
neither moral nor religious motives can be relied on as an adequate
control. They are not found to be such on the injustice and violence of
individuals, and lose their efficacy in proportion to the number combined
together, that is, in proportion as their efficacy becomes needful.
From this view of the subject it may be concluded that a pure democracy,
by which I mean a society consisting of a small number of citizens, who
assemble and administer the government in person, can admit of no cure
for the mischiefs of faction. A common passion or interest will, in almost
every case, be felt by a majority of the whole; a communication and
concert result from the form of government itself; and there is nothing to
check the inducements to sacrifice the weaker party or an obnoxious
individual. Hence it is that such democracies have ever been spectacles of
turbulence and contention; have ever been found incompatible with
personal security or the rights of property; and have in general been as
short in their lives as they have been violent in their deaths. Theoretic
politicians, who have patronized this species of government, have
erroneously supposed that by reducing mankind to a perfect equality in
their political rights, they would, at the same time, be perfectly equalized
and assimilated in their possessions, their opinions, and their passions.
A republic, by which I mean a government in which the scheme of
representation takes place, opens a different prospect, and promises the
cure for which we are seeking. Let us examine the points in which it varies
from pure democracy, and we shall comprehend both the nature of the
cure and the efficacy which it must derive from the Union.
The two great points of difference between a democracy and a republic
are: first, the delegation of the government, in the latter, to a small number
of citizens elected by the rest; secondly, the greater number of citizens,
and greater sphere of country, over which the latter may be extended.
The effect of the first difference is, on the one hand, to refine and enlarge
the public views, by passing them through the medium of a chosen body of
citizens, whose wisdom may best discern the true interest of their country,
and whose patriotism and love of justice will be least likely to sacrifice it to
temporary or partial considerations. Under such a regulation, it may well
happen that the public voice, pronounced by the representatives of the
people, will be more consonant to the public good than if pronounced by
the people themselves, convened for the purpose. On the other hand, the
effect may be inverted. Men of factious tempers, of local prejudices, or of
sinister designs, may, by intrigue, by corruption, or by other means, first
obtain the suffrages, and then betray the interests, of the people. The
question resulting is, whether small or extensive republics are more
favorable to the election of proper guardians of the public weal; and it is
clearly decided in favor of the latter by two obvious considerations:
In the first place, it is to be remarked that, however small the republic may
be, the representatives must be raised to a certain number, in order to
guard against the cabals of a few; and that, however large it may be, they
must be limited to a certain number, in order to guard against the
confusion of a multitude. Hence, the number of representatives in the two
cases not being in proportion to that of the two constituents, and being
proportionally greater in the small republic, it follows that, if the proportion
of fit characters be not less in the large than in the small republic, the
former will present a greater option, and consequently a greater probability
of a fit choice.
In the next place, as each representative will be chosen by a greater
number of citizens in the large than in the small republic, it will be more
difficult for unworthy candidates to practice with success the vicious arts by
which elections are too often carried; and the suffrages of the people being
more free, will be more likely to centre in men who possess the most
attractive merit and the most diffusive and established characters.
It must be confessed that in this, as in most other cases, there is a mean,
on both sides of which inconveniences will be found to lie. By enlarging too
much the number of electors, you render the representatives too little
acquainted with all their local circumstances and lesser interests; as by
reducing it too much, you render him unduly attached to these, and too
little fit to comprehend and pursue great and national objects. The federal
Constitution forms a happy combination in this respect; the great and
aggregate interests being referred to the national, the local and particular
to the State legislatures.
The other point of difference is, the greater number of citizens and extent
of territory which may be brought within the compass of republican than government; of
democratic and it is this circumstance principally which
renders factious combinations less to be dreaded in the former than in the
latter. The smaller the society, the fewer probably will be the distinct
parties and interests composing it; the fewer the distinct parties and
interests, the more frequently will a majority be found of the same party;
and the smaller the number of individuals composing a majority, and the
smaller the compass within which they are placed, the more easily will they
concert and execute their plans of oppression. Extend the sphere, and you
take in a greater variety of parties and interests; you make it less probable
that a majority of the whole will have a common motive to invade the rights
of other citizens; or if such a common motive exists, it will be more difficult
for all who feel it to discover their own strength, and to act in unison with
each other. Besides other impediments, it may be remarked that, where
there is a consciousness of unjust or dishonorable purposes,
communication is always checked by distrust in proportion to the number
whose concurrence is necessary.
Hence, it clearly appears, that the same advantage which a republic has
over a democracy, in controlling the effects of faction, is enjoyed by a large
over a small republic,--is enjoyed by the Union over the States composing
it. Does the advantage consist in the substitution of representatives whose
enlightened views and virtuous sentiments render them superior to local
prejudices and schemes of injustice? It will not be denied that the
representation of the Union will be most likely to possess these requisite
endowments. Does it consist in the greater security afforded by a greater
variety of parties, against the event of any one party being able to
outnumber and oppress the rest? In an equal degree does the increased
variety of parties comprised within the Union, increase this security. Does
it, in fine, consist in the greater obstacles opposed to the concert and
accomplishment of the secret wishes of an unjust and interested majority?
Here, again, the extent of the Union gives it the most palpable advantage.
The influence of factious leaders may kindle a flame within their particular
States, but will be unable to spread a general conflagration through the
other States. A religious sect may degenerate into a political faction in a
part of the Confederacy; but the variety of sects dispersed over the entire
face of it must secure the national councils against any danger from that
source. A rage for paper money, for an abolition of debts, for an equal
division of property, or for any other improper or wicked project, will be less
apt to pervade the whole body of the Union than a particular member of it;
in the same proportion as such a malady is more likely to taint a particular
county or district, than an entire State.
In the extent and proper structure of the Union, therefore, we behold a
republican remedy for the diseases most incident to republican
government. And according to the degree of pleasure
FEDERALIST No. 51
The Structure of the Government Must Furnish the Proper Checks
and Balances Between the Different DepartmentsFrom the New York
Packet. Friday, February 8, 1788. Alexander Hamilton or James
Madison
To the People of the State of New York:
TO WHAT expedient, then, shall we finally resort, for maintaining in
practice the necessary partition of power among the several departments,
as laid down in the Constitution? The only answer that can be given is, that
as all these exterior provisions are found to be inadequate, the defect must
be supplied, by so contriving the interior structure of the government as
that its several constituent parts may, by their mutual relations, be the
means of keeping each other in their proper places. Without presuming to
undertake a full development of this important idea, I will hazard a few
general observations, which may perhaps place it in a clearer light, and
enable us to form a more correct judgment of the principles and structure
of the government planned by the convention.
In order to lay a due foundation for that separate and distinct exercise of
the different powers of government, which to a certain extent is admitted
on all hands to be essential to the preservation of liberty, it is evident that
each department should have a will of its own; and consequently should be
so constituted that the members of each should have as little agency as
possible in the appointment of the members of the others. Were this
principle rigorously adhered to, it would require that all the appointments
for the supreme executive, legislative, and judiciary magistracies should be
drawn from the same fountain of authority, the people, through channels
having no communication whatever with one another. Perhaps such a plan
of constructing the several departments would be less difficult in practice
than it may in contemplation appear. Some difficulties, however, and some
additional expense would attend the execution of it. Some deviations,
therefore, from the principle must be admitted. In the constitution of the
judiciary department in particular, it might be inexpedient to insist
rigorously on the principle: first, because peculiar qualifications being
essential in the members, the primary consideration ought to be to select
that mode of choice which best secures these qualifications; secondly,
because the permanent tenure by which the appointments are held in that
department, must soon destroy all sense of dependence on the authority
conferring them.
It is equally evident, that the members of each department should be as
little dependent as possible on those of the others, for the emoluments
annexed to their offices. Were the executive magistrate, or the judges, not
independent of the legislature in this particular, their independence in
every other would be merely nominal.
But the great security against a gradual concentration of the several
powers in the same department, consists in giving to those who administer
each department the necessary constitutional means and personal motives
to resist encroachments of the others. The provision for defense must in
this, as in all other cases, be made commensurate to the danger of attack.
Ambition must be made to counteract ambition. The interest of the man
must be connected with the constitutional rights of the place. It may be a
reflection on human nature, that such devices should be necessary to
control the abuses of government. But what is government itself, but the
greatest of all reflections on human nature? If men were angels, no
government would be necessary. If angels were to govern men, neither
external nor internal controls on government would be necessary. In
framing a government which is to be administered by men over men, the
great difficulty lies in this: you must first enable the government to control
the governed; and in the next place oblige it to control itself. A dependence
on the people is, no doubt, the primary control on the government; but
experience has taught mankind the necessity of auxiliary precautions.
This policy of supplying, by opposite and rival interests, the defect of better
motives, might be traced through the whole system of human affairs,
private as well as public. We see it particularly displayed in all the
subordinate distributions of power, where the constant aim is to divide and
arrange the several offices in such a manner as that each may be a check
on the other that the private interest of every individual may be a sentinel
over the public rights. These inventions of prudence cannot be less
requisite in the distribution of the supreme powers of the State.
But it is not possible to give to each department an equal power of selfdefense. In republican government, the legislative authority necessarily
predominates. The remedy for this inconveniency is to divide the
legislature into different branches; and to render them, by different modes
of election and different principles of action, as little connected with each
other as the nature of their common functions and their common
dependence on the society will admit. It may even be necessary to guard
against dangerous encroachments by still further precautions. As the
weight of the legislative authority requires that it should be thus divided,
the weakness of the executive may require, on the other hand, that it
should be fortified. An absolute negative on the legislature appears, at first
view, to be the natural defense with which the executive magistrate should
be armed. But perhaps it would be neither altogether safe nor alone
sufficient. On ordinary occasions it might not be exerted with the requisite
firmness, and on extraordinary occasions it might be perfidiously abused.
May not this defect of an absolute negative be supplied by some qualified
connection between this weaker department and the weaker branch of the
stronger department, by which the latter may be led to support the
constitutional rights of the former, without being too much detached from
the rights of its own department?
If the principles on which these observations are founded be just, as I
persuade myself they are, and they be applied as a criterion to the several
State constitutions, and to the federal Constitution it will be found that if the
latter does not perfectly correspond with them, the former are infinitely less
able to bear such a test.
There are, moreover, two considerations particularly applicable to the
federal system of America, which place that system in a very interesting
point of view.
First. In a single republic, all the power surrendered by the people is
submitted to the administration of a single government; and the
usurpations are guarded against by a division of the government into
distinct and separate departments. In the compound republic of America,
the power surrendered by the people is first divided between two distinct
governments, and then the portion allotted to each subdivided among
distinct and separate departments. Hence a double security arises to the
rights of the people. The different governments will control each other, at
the same time that each will be controlled by itself.
Second. It is of great importance in a republic not only to guard the society
against the oppression of its rulers, but to guard one part of the society
against the injustice of the other part. Different interests necessarily exist in
different classes of citizens. If a majority be united by a common interest,
the rights of the minority will be insecure. There are but two methods of
providing against this evil: the one by creating a will in the community
independent of the majority that is, of the society itself; the other, by
comprehending in the society so many separate descriptions of citizens as
will render an unjust combination of a majority of the whole very
improbable, if not impracticable. The first method prevails in all
governments possessing an hereditary or self-appointed authority. This, at
best, is but a precarious security; because a power independent of the
society may as well espouse the unjust views of the major, as the rightful
interests of the minor party, and may possibly be turned against both
parties. The second method will be exemplified in the federal republic of
the United States. Whilst all authority in it will be derived from and
dependent on the society, the society itself will be broken into so many
parts, interests, and classes of citizens, that the rights of individuals, or of
the minority, will be in little danger from interested combinations of the
majority. In a free government the security for civil rights must be the same
as that for religious rights. It consists in the one case in the multiplicity of
interests, and in the other in the multiplicity of sects. The degree of security
in both cases will depend on the number of interests and sects; and this
may be presumed to depend on the extent of country and number of
people comprehended under the same government. This view of the
subject must particularly recommend a proper federal system to all the
sincere and considerate friends of republican government, since it shows
that in exact proportion as the territory of the Union may be formed into
more circumscribed Confederacies, or States oppressive combinations of
a majority will be facilitated: the best security, under the republican forms,
for the rights of every class of citizens, will be diminished: and
consequently the stability and independence of some member of the
government, the only other security, must be proportionately increased.
Justice is the end of government. It is the end of civil society. It ever has
been and ever will be pursued until it be obtained, or until liberty be lost in
the pursuit. In a society under the forms of which the stronger faction can
readily unite and oppress the weaker, anarchy may as truly be said to
reign as in a state of nature, where the weaker individual is not secured
against the violence of the stronger; and as, in the latter state, even the
stronger individuals are prompted, by the uncertainty of their condition, to
submit to a government which may protect the weak as well as
themselves; so, in the former state, will the more powerful factions or
parties be gradnally induced, by a like motive, to wish for a government
which will protect all parties, the weaker as well as the more powerful. It
can be little doubted that if the State of Rhode Island was separated from
the Confederacy and left to itself, the insecurity of rights under the popular
form of government within such narrow limits would be displayed by such
reiterated oppressions of factious majorities that some power altogether
independent of the people would soon be called for by the voice of the very
factions whose misrule had proved the necessity of it. In the extended
republic of the United States, and among the great variety of interests,
parties, and sects which it embraces, a coalition of a majority of the whole
society could seldom take place on any other principles than those of
justice and the general good; whilst there being thus less danger to a
minor from the will of a major party, there must be less pretext, also, to
provide for the security of the former, by introducing into the government a
will not dependent on the latter, or, in other words, a will independent of
the society itself. It is no less certain than it is important, notwithstanding
the contrary opinions which have been entertained, that the larger the
society, provided it lie within a practical sphere, the more duly capable it
will be of self-government. And happily for the REPUBLICAN CAUSE, the
practicable sphere may be carried to a very great extent, by a judicious
modification and mixture of the FEDERAL PRINCIPLE.
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4.1 Example Counting until OverflowThe following program count until an overflow condition is met. The number displayed is the last numberthat was added before the number overflowed into the negative side of the number line. Note the algorithmfirst cou
UCF - EGN - 3210
/ program7_4.cpp : Defines the entry point for the console application./#include "stdafx.h"/ program 7.3#include#include"stdio.h""stdlib.h"#define#defineTRUEcharFILEintintcharbuffer[10];*fp;i;icode;code;FALSE 0!FALSEvoidmain( inta
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8.1 Ex Parsing using a Finite State Machine (FSM) algorithmA finite state machine also known as a finite state acceptor is a theoretical machine or algorithmthat uses a table to determine its current state and its action. The system is described with st
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#include#include"stdio.h""string.h"struct datecfw_char month[10];intday;intyear;void init(char*m, int d, int y)cfw_strcpy (month, m);day = d;year = y;void;print()cfw_printf("%10s/%2d/%2d",month, day, year);structrecordcfw_char n
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9.1 Advanced StructuresAdvanced structures are a C+ feature that allows one to put functions as field elementsinto a structure. Consider the datetype from before.Struct datetypecfw_intmonth;intday;intyear;;struct datetypedate;date.month = 7;
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#include#include"iostream.h""string.h"class Personcfw_private:intcharpublic:;age;*name;Person(int a, char *s);~Person( );void display( );void assign(int a, char *s);void operator = (Person &other_object);friendvoid show_older(Person &a,
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To run a program using CodeWarrior we first select the application from the start menu.We get:Next we select new from the File menu and get:Next we select Win32 C/C+ Application Stationary and type HW1 in the Project name: boxto get:We next click the
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Variations of counting combinationsCombining our result for counting combinations, some logic, the sum rule and the product rule, we can handle more sophisticated counting questions. Take the following, for example: Let S= cfw_1, 2, 3, ., 30. How many su
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Outline of COT 3100 material for first exam I. Logic A. Symbols(, and ) B. Truth Tables C. Logic Laws D. Methods of showing equality of logical expressions E. Implication Rules F. Contrapositive of a stmt. G. Quantifiers II. Sets A. Symbols( , , , , , , a
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Fundamentals of LogicStatements/Propositions Sentences that are true or false but not both. (Just like a simple boolean expression or conditional expression in a programming language.) For our purposes, statements will simply be denoted by lowercase lett
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Fundamental Theorem of ArithmeticEven though this is one of the most important results in all of Number Theory, it is rarely included in most high school syllabi (in the US) formally. Interestingly enough, almost everyone has an intuitive notion of this
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Probability NotesThe Let's Make a Deal Problem is as follows: There is a car behind one of three doors, A, B or C, and a goat behind the other two. A contestant picks one of the three doors. The host then reveals one of the other two doors and shows a go
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Composition of Relations In math class, given two functions f(x) and g(x), you probably had to figure out the composition of the functions, which is denoted either by f(g(x) OR fg(x). Basically, the way this worked is that you "plugged in" your original x
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/Discreet Programming assignment 1/Programmed in C+ for educational purposes/ the only c+ - specific syntax used is the i/o./By David Callies//1/9/08#include<iostream>uusing namespace std;#define#define#define##defineBIT_ABIT_BBIT_CBIT_
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Honors Introduction to Discrete Structures COT 3100H Exam #1: Logic, Sets Date: 1/31/08 Solutions 1) (10 pts) Complete the following truth table. Please designate expressions for the intermediate columns in the table. (r p ) p F F F F T T T T q F F T T F
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COT 3100 Final Exam 12/5/06 Name: _ Lecturer: Arup Guha TA: _ Section: _(Note: You will have 2 hours and 50 minutes for this exam. Make sure to read AND follow all the directions. If you need extra room for your work, put it on the last page of the exam
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COT 3100H Spring 2008 Homework #1 Solutions1) a) p 0 0 1 1 b) p 0 0 0 0 1 1 1 1 c) p 0 0 0 0 1 1 1 1 q 0 0 1 1 0 0 1 1 r 0 1 0 1 0 1 0 1 pr 1 1 1 1 0 1 0 1 q(pr) 0 0 1 1 0 0 0 1 (q(pr) 1 1 0 0 1 1 1 0 p (q(pr) 0 0 0 0 1 1 1 0 q 0 0 1 1 0 0 1 1 r 0 1 0 1
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Spring 2008 COT 3100 Homework #3 Grading Criteria - 100 points 1) a) 10 pts 6 pts to prove subset, 4 pts to prove proper b) 10 pts 5 pts to say false, 5 pts for the counter example 2) a) 10 pts 4 pts for first step, 3 pts for steps 2 and 3 b) 15 pts 3 pts
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COT 3100H Spring 2008 Homework #4 Solutions1) The House currently has 199 Republicans, 232 Democrats and four vacancies. (Nathan corrected my information.) Answer the following questions about forming committees in the House. (a) How many committees can
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Spring 2008 COT 3100 Homework #5 Grading Criteria - 100 points 1) 15 points 5 pts for stay, 10 pts for switch ( 3 pts for 4/5, 3 pts for multiply, 4 pts for 1/3) 2) 10 points 4 points for numerator, 3 pts for second term in denominator, 1pt for adding the
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COT 3100H Spring 2008 Homework #1 Assigned: 1/8/08 Due: 1/15/081) Write out a truth table for the following logical expressions: a) [ p ( p q )] q c) p (q (p r ) 2) Determine all truth value assignments for the primitive statements p, q, r, s, t that mak
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/** Name: Amy Hoover* Assignment: Homework 1* Class: COT 3100H* Date: 1/15/08*/import java.util.*;ppublic class Homework1 cfw_byte op1 = 0;byte op2 = 0;bbyte op3 = 0;/Homework object stores the three operators set by the userpublic Homework1
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COT 3100H Spring 2008 Homework #2 Assigned: 1/15/08 Due: 1/22/081) Prove that the fourth power of an odd integer leaves a remainder of 1 when divided by 16. (Hint: You may want to first prove that the expression a(a+1) or a(3a+1) is even for all integers
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COT 3100H Spring 2008 Homework #7 Assigned: 3/4/08 (Tuesday) Due: 3/6/08 (Thursday)1) Find GCD(729, 321) using Euclid's Algorithm. 2) Find all integer solutions for x and y to the equation 729x + 321y = gcd(729, 321). 3) Find all integer solutions for x
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/Scott Dyl/COT3100H//Homework #2import java.util.Scanner;import java.util.TreeSet;iimport java.util.Vector;ppublic class Hw2 cfw_ppublic static void main(String[] args) cfw_TreeSet<Integer> setA = new TreeSet<Integer>();TTreeSet<Integer> set
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Sample Counting ProblemsDisguised questions of combinations and permutations 1) A particle starts at the origin of the Cartesian plane and travels to the point (6, 7). It always moves parallel to the x or y axis and always moves in the positive direction
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public class MyPoint extends java.awt.Point cfw_private static final long serialVersionUID = 1;int x;int y;public MyPoint(int x, int y) cfw_super(x, y);public String toString() cfw_String rval = ";rval += "(" + (int)this.getX() + "," + (int)this.
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/** Name: Amy Hoover* Assignment: Homework 2* Class: COT 3100H* Date: 1/22/07*/iimport java.util.*;public class SetOperations cfw_/Declares several program constantspublic static final int DEFAULT = -2;public static final int END_OF_STRING = -1
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COT 4210-01 Discrete Structures II - Fall 2011 SyllabusClass Time: Tuesday, Thursday 1:30-2:45pmClass Location: HEC 118Lecturer: Arup GuhaOffice: HEC 240Email: dmarino@cs.ucf.eduPhone Number: 407-823-1062Office Hours: MW 2:15-3pm, 5-5:45pm, TR 11am
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/ Arup Guha/ 3/23/05/ Example illustrating reduction of ATM to HALT.public class HALT cfw_/ doesHalt is supposed to return true if M halts on w, false otherwise.public static boolean doesHalt(String encodeM, String w) cfw_if (encodeM.charAt(0) = w.
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COT 4210 Homework #1 Grading Criteria1) 6 pts totalAll transitions: 3 pts total give partial as you see fitLabeling accept states: 2 pts, 1 for eachStart state label: 1 pt2) 10 pts1 pt for having 6 states1 pt for having the start and accept state l
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COT 4210 (Proof) Homework #1: Regular LanguagesDue Date: Thursday September 8, 2011Note: Unless otherwise noted, assume the alphabet for each language is cfw_0, 1.1) Draw the state diagram for the DFA formally described below:cfw_Q, , , q0, F whereQ
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COT 4210 Lecture 1, 1/12/05Notetakers: Frank Cama & Enrique Montealegreinput:5 nickels10 dimes5 states: 0, 5, 10, 15, 20ex1:initial state is 0machine takes dime, state is now 10machine takes dime, state is now 20machine takes dime, output soda!
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Regular Operationsby Ariel De PradaRegular Operations (let A and B be languages)U union; A U B = cfw_x | x A V x Bo concatenation; A o B = cfw_xy | x A y BExample: 01101E A 01101 B0 A 1101 B01 A 101 B011 A 01 B0110 A 1 B01101 A E B* - star; A*