MAT 243 HW 3 SOLUTIONS
(1) (4 pts) Fill in the blank in the statements below:
(a) P (S) is the set containing all subsets of S i.e., P (S) = cfw_X | X S
(b) A B = cfw_x | x A x B
/
(c) A function f :
6.1-6.2-6.3-6.4
Quiz 7 due Wednesday April 1st
(1) Given 10 chips each of them of different colors (including red and white). For each of the following
questions explain your answer. You should use fa
MAT 243 WRITTEN HOMEWORK 1
NAME: Solutions
(1) Fill in the blank in the statements below:
(a) Two propositions are logically equivalent if and only if they have the same truth values.
(b) A tautology
P(n) = (22n-1 = a multiple of 3 for any positive integer n).
P(n) = (22 n-1 = 3k) for some integer k
Base case: 22(1)-1 = 3k
3 = 3k, k =1 is an integer, so base case is true
Inductive step: Suppose P(
Base Case: 1 divided by 4 leaves a remainder of 1.
n = aq+r
1 = 4*a+1, there exists a so that this is true (a=0), thus base case is true
Structural Induction: By definition, if n= 4a+1, there exists a
MAT 243 ONLINE WRITTEN HW 6 SOLUTIONS
(1) (4 pts) Fill in the blank in the statements below:
(a) When making a sequence of choices in counting we are using the Product Rule.
(b) We are using the Sum R
Juan Espino
Kolossa MAT 243 ONLINE A Spring 2017
Assignment Unit3 Predicates and Quantifiers due 01/15/2017 at 11:59pm MST
2. !x(x + 3 = 2x)
3. !x(x = x + 1)
4. !x(x > 1)
1. (1 point)
Let P(x) be the
Juan Espino
Kolossa MAT 243 ONLINE A Spring 2017
Assignment Unit7 Set Operations due 01/28/2017 at 11:59pm MST
Correct Answers:
[-6,2)
(-1,0)
[-6,1]
(-infinity,-1] U [0,infinity)
(-infinity,-6) U
ASU SoMSS MAT 243 Mohacsy Version A TEST 1 Spring 2017
MAT 243 Spring 2017 Exam 1 A
Instructor: Mohacsy
NAME: (PRINTH) QAA LOW
Honor Statement:
By signing below you confirm that you have neither given
MAT 243 Topics
Foundations:
Logic, Propositions, Equivalences, Predicates, Quantiers, Sets,
Set Operations, Functions, Sequences and Summations, Growth of Functions.
Fundamentals
Methods of Proof
Coun
Juan Espino
Kolossa MAT 243 ONLINE A Spring 2017
Assignment Unit2 Propositional Equivalence due 01/12/2017 at 11:59pm MST
1. (1 point) Complete the following truth table by filling in
the blanks with
Mat 243 Ionascu Test II Review
SHORT STORY of the TOPICS to be covered on Test II
Section 2.3 Functions: understand the definition of a function, domain, codomain, range; what it mean for
a function t
MAT 243 WRITTEN HOMEWORK 1
(1) Fill in the blank in the statements below:
(a) Two propositions are logically equivalent if and only if they have the same truth values.
(b) A tautology is a proposition
MAT 243 ONLINE WRITTEN HW 5 SOLUTIONS
NAME:
(1) (4 pts) Fill in the blank in the statements below:
(a) In an inductive proof verifying the condition for n = 1 (or the lowest possible value)
is called
MAT 243 Test 1 Practice solutions
1.
(a)
(b)
(c)
(d)
sufficient
necessary
necessary
sufficient
2.
Consider the statement if x>1 then x2>1
3.
Converse: if x2>1 then x>1
False Counter ex: let x= -3.
Nec
Discrete Mathematics
Summer 03
Assignment # 3 : Solutions
Section 3.1
12.The sum of any two odd integers is even.
Given: Two odd numbers a and b.
Prove: a+b is even.
From definition of odd number, a=2
KUNAL LANJEWAR
1.
Let,
P be the set of all people
L(x) be the predicate "X likes ice cream"
K(x) be the predicate "X is a kid"
i.
Every kid loves ice cre
MAT 243 ONLINE WRITTEN HW 5 SOLUTIONS
NAME:
(1) (4 pts) Fill in the blank in the statements below:
(a) In an inductive proof verifying the condition for n = 1 (or the lowest possible value)
is called
Juan Espino
Assignment Unit15 Recursion due 02/12/2017 at 11:58pm MST
4. (1 point) For the sequence an = an1 + an2 and
a1 = 5, a2 = 6,
;
its first term is
its second term is
;
its third term is
;
its
Juan Espino
Kolossa MAT 243 ONLINE A Spring 2017
Assignment Unit1 Propositional Logic due 01/12/2017 at 11:59pm MST
1. (1 point)
Enter T for each true proposition, F for each false proposition and N f
1.6 Problem 5 (a): 2 is an integer greater than 1, so 2 is in the set. (b): 2 is not the square of an integer, so 2 is not in the set.
(c): The set {2, {2} does contain 2 (it's lis
Sol MAT 243 Homework 9
0. Convert 12021 to duodecimal (base 12) using repeated application of the division algorithm.
Show all your steps.
12021 = 1001 12 + 9
1001 = 83 12 + 5
83 = 6 12 + 11
Therefore
REVIEW FOR TEST 1, MAT 243, FALL 2013
The exam covers sections 1.1, 1.3, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, 2.3, and 2.4.
Test 1, October 2, 2013
Think of this review as a starting point for studying for E
Solutions to exam 1
1. Construct the truth table for the following proposition:
(p q ) (p r)
Solution:
p
T
T
T
T
F
F
F
F
q
T
T
F
F
T
T
F
F
r
T
F
T
F
T
F
T
F
p q p r p r (p q ) (p r)
T
FF
T
T
T
FT
F
F
Assignment Unit2 Propositional Equivalence
1. (1 pt) Complete the following truth table by filling in the
blanks with T or F as appropriate.
p q p!q :p :q :q!:p
TT
TF
FT
FF
p!q and :q!:p are
_ A. not
Mathematics 243 Discrete Mathematical Structures
Professor Tim Callahan Time: T 3:154:30 in PSA 307. Book: Discrete Mathematics and Its Applications, by Kenneth H. Rosen, 5th ed. You should read the r
MAT 243 Proof paper (1.6-1.7) Last Name:
OpM'h'Oi/u
Due: Wednesday Feb 11 S First Name:
1- (6 points) Prove that if an:2 is an irrational number then i is also irrational,
COM1_:_-POS:1LFOM' 3 m 3% 1'
MAT 243 Online Written Homework
Assignments for Week 3 (units 6-9)
1. Prove or disprove: = [1,3) (2,3] is the empty set.
We prove that is not empty by showing existence of an element in .
Let x=2.5. T
MAT 243 Online Written Homework
Assignments for Week 1 (units 1-3)
1. Show that ( ) ( ) is logically equivalent to using logical equivalence
rules. Name each rule. You will get no credit for any other
MAT 243 Online Written Homework
Assignments for Week 4 (units 10-13)
0. A function f(x) is big-O of g(x) if and only if there exist constants C and k such that
|f(x)| < C|g(x)| if x>k.
A function f(x)
MAT 243 Online Written Homework Assignments
for Week 2 (units 4-5) Solutions
(A natural number is a positive integer: 1,2, 3, etc.)
1. Formalize the following argument by using the given predicates an
MAT 243 ONLINE WRITTEN HW 6
(1) Fill in the blank in the statements below:
(a) When making a sequence of choices in counting we are using the
(b) We are using the Sum Rule when choosing among
(c) We a