Math 140: Quiz Solutions
Quiz 1
Problem 1: Show the following logical equivalence holds, by truth tables.
p q (p q)
Solution:
p
T
T
F
F
q
T
F
T
F
q
F
T
F
T
pq
F
T
T
T
pq
T
F
F
F
(p q)
F
T
T
T
Problem 2: Negate the following statements using DeMorgans Law
Math 140: Quiz 6,7,8
Quiz 8
Problem 1: Draw the graph associated with the
0
2
1
adjacency matrix
2 1
1 2
2 0
label the vertices associated with the first, second and third row, v1 , v2 , and v3 , respectively.
Problem 2: How many walks of length 2 are t
Math 140: Quiz 6,7,8
Quiz 6
Problem 1: Prove the following by contradiction: There is no largest even number.
Problem 2: Prove the following. Proof by contrapositive would be the most immediate approach:
Suppose m and n are integers. If mn is odd, then m
Math 140: Quiz 6,7,8
Quiz 7
Problem 1: Consider the following graph.
1. What is the total degree of the graph?
2. Find an Euler circuit on the graph. Be certain to label the edges in order, as the appear in your
circuit.
Math 140: Practice Test 1
Problem 1: Create truth tables for the following statements:
a. p (q p)
b. q (p q)
c. (q p).
d. r (p q)
Problem 2: Show the following statements are logically equivalent, by use of a truth table
(p q) q (p q)
Problem 3: Find the
Math 140: Practice Test 1
Problem 1: Create truth tables for the following statements:
a. p (q p)
Solution:
p
T
T
F
F
q
T
F
T
F
p
F
F
T
T
q p
F
T
T
T
p
T
T
F
F
q
T
F
T
F
pq
T
F
T
T
p
T
T
F
F
q
T
F
T
F
p
F
F
T
T
p (q p)
T
T
T
T
b. q (p q)
Solution:
q
F
T
F
Math 140: Homework 2
Name:
Instructions: Due Thursday April 14th.
Problem 1.
a. Show that the following statements are logically equivalent, by use of a truth table.
(1) p (q r)
(2) (p q) r
(3) (p r) q
b. Use the logical equivalence of the forms in part a
Math 140: Homework List
Name:
Instructions: Print out this page and staple any work to the back. Due Thursday April 7th in class.
Problem 1: Create truth tables for the following statements.
a. (p q) p
b. (p q) p
c. (p q) (q r)
Problem 2: Show that the fo
Math 140: Quiz Solutions
Quiz 4
Theorem: Suppose a, b Z. If a is odd and b is even, then 3b 5a is odd.
Proof: Suppose a is odd and b is even. Let k Z such that a = 2k + 1 and let j Z such that b = 2j.
Then
3b 5a = 3(2j) 5(2k + 1)
= 6j (10k + 5)
= 6j 10k 5
Math 140: Quiz Solutions
Quiz 3:
Problem 1: Write the negations of the following quantified statements. Simplify the expression until
the negation symbol isnt present; i.e. rewrite expressions such as (x = 2) as x 6= 2.
a. n Z (x2 > 0)
Solution:
n Z (x2
Math 140: Quiz Solutions
Quiz 2:
Problem 1: Write the contrapositive of the following conditional statements; simplify the expression
using DeMorgans laws, etc., until negation symbols appear in front of variables only (and not compound
statements).
a. (p