Mat 243
week 4 Homework
0.
Means that there is some constant C and some constant k such that | ()| | ()| for all > .
means that there are positive constants and such that | ()| | ()| for all > .
means
Block Conversion from Binary to Octal
We have learned that we can block-convert a binary number to octal by grouping
the binary number into blocks of 3 digits (going from right to left, perhaps
paddin
Jose Duran-Cruz Written Homework Week #5
1.
a.
b.
c.
d.
base step for base case
inductive hypothesis
some n 1
equation that defines the elements of a sequence recursively
2. Proof
Basic case for J = 1
Jose Duran-Cruz Written Homework Week #7
1.
a. =1 | | -
1
<
| | + 1 < | | + (1)+1 |1 2 |
b. sample space
c. equally likely
d. for all elements a, b, and c in A, if (a,b) R and (b,c) R the (a,c) R
2
Jose Duran-Cruz Written Homework Week #6
1.
a.
b.
c.
d.
product
mutually exclusive
ordered
if there are k boxes and you place N objects into them then at least one box will contain at
least
objects.
2
Jose Duran-Cruz Written Homework Week #2
1. Let P be the set of all Dogs
Let D(x) be the predicate x is a Dog
Let M(x) be the predicate x eats meat
1. x P, D(x) => M(x), Premise
2. ~ M(Bill), Premise
Mat 243 Written Homework 1
Name:
1.
A. If and only if they have identical truth tables.
B. a propositional expression that yields a true statement regardless of what statements replace its
variables.
Math 243
Week 3
1.
a. x,y EA, (f(x)=f(y) (x=y)
b. for some (x,y)EA , f(x)=f(y) x=y
c. every output element is assigned atleast once
d. atleast one output element remains unassigned
e. (x,y) EA, (x<y)f
Mat 243
Week 7 Homework
1.
a.
b.
Thesetofallpossibleoutcomesiscalledthesample spacefortheexperiment.
c.
If outcomes are equally likely, then the probability of an event occurring is the number
in the
Mat 243
Week 5
1.
a. Base step or base case
b. and c. inductive hypothesis and n1
d. an equation that defines the elements of a sequence recursively
2.
Mat 243
Week 5
3.
We need to prove that 3nn!, fo
Mat 243
Week 2
1.
a)there is proof of it
b)modus ponens
c)fallacy of affirming the conclusion
d)a theorem that follows easily from another theorem
e) Direct: we will consider p statement and then show
Week 3 Extra Credit
ABijectiveCompositionofNotBijectiveFunctions
h
A
B
g
C
f
let g be not one-one
then a1 a2 s.t. g(a1)= g(a2)
now h(a1)= fg(a1)=f(g(a2)
=h(a2)
Thus h cannot be one one
let f be not on
Jose M Duran-Cruz Written Homework Week #1
1.
e
2.
a
3.
c
4.
5.
a. If I live to the age of 120, then I dont smoke.
b. If there are rainbows, then it must be raining.
c. If the stars can be seen, then