Discrete Mathematics Answers

6. Select the statement that is the negation of “You wear matching socks to the interview or you don’t get
hired.”
A. You don’t wear matching socks to the interview or you get hired.
B. You don’t wear matching socks to the interview and you get hired.
C. You don’t wear matching socks to the interview and you don’t get hired.
D. If you don’t wear matching socks to the interview, then you don’t get hired.

7-13: Find the Truth Value (show your solution)
7. Suppose p is false, q is false, s is true. Find the truth value of (s ∨ p) ∧ (q∧ ┐s)
8. Suppose p is true, q is true, r is false, s is false. Find the truth value of (s ∨ p) ∧ (┐r ∨ ┐s)
9. Suppose p is true, q is true, s is false. Find the truth value of (┐s ∨ p) ∨ (q ∧ ┐s)
10. Suppose p is false, s is false, r is true. Find the truth value of ┐ [(s ∧ p) ∨ ┐r]
11. Suppose p is false, q is true, s is true. Find the truth value of (p ∧ ┐q) ∨ ┐s
12. Suppose p is false, q is true, r is false. Find the truth value of (p ∨ ┐q) ∨ r
13. Suppose p is true, q is true, r is true, s is false. Find the truth value of (┐p ∨ s) ∨ (s ∧ r)
14-15: Make a truth table for the given expression.
14. (┐p ∧ q) ∨ (p ∧ ┐q)
15. (┐p ∧ q) (┐p ∨ q)

4. Suppose p is the statement 'I play softball' and q is the statement 'The moon is 250,000 miles from Earth.' Select
the correct statement corresponding to the symbols ┐p ∧ q.
A. I don't play softball and the moon is 250,000 miles from Earth.
B. It is not the case that either I play softball or the moon is 250,000 miles from Earth.
C. I don't play softball or the moon is 250,000 miles from Earth.
D. It is not the case that both I play softball and the moon is 250,000 miles from Earth.

5. Select the statement that is the negation of “Coach Spurrier is charming and Coach Spurrier is modest.”
A. Coach Spurrier is not charming and Coach Spurrier is not modest.
B. Coach Spurrier is not charming or Coach Spurrier is not modest.
C. Coach Spurrier is not charming and Coach Spurrier is modest.
D. Let’s get serious for a minute.

Instruction: Write only the letter of your answer.
1. Suppose p is the statement 'You need a credit card' and q is the statement 'I have a nickel.' Select the correct
statement corresponding to the symbols ┐(p ∨ q).
A. You don't need a credit card and I have a nickel.
B. It is not the case that either you need a credit card or I have a nickel.
C. You don't need a credit card or I have a nickel.
D. None of these.
2. Suppose p is the statement 'There are 1,000 meters in one kilometer' and q is the statement 'You will give me a
cake.' Select the correct symbolization for the statement 'There are 1,000 meters in one kilometer or you will
not give me a cake'.
A. ┐(p∧q) B. p∧┐q C. p∨┐q D. None of these

3. Suppose p is the statement 'There are 1,000 meters in one kilometer' and q is the statement 'You will order a
burrito.' Select the correct symbolization for the statement 'There are not 1,000 meters in one kilometer and
you won't order a burrito'.
A. ┐p∧┐q B. ┐(p∧q) C. ┐p∨┐q D. None of these

Define the following terms with proper diagrams:

a. Degree of a node in a graph
b. Copies of binary trees

Define the following terms with proper example:

a. Relatively prime integers
b. Hadamard Matrix

Explain graph isomorphism with proper diagrams.

The recursive definition of a function X is given as:
f(0)=5 and f(n)=f(n-2)+5
Now, find out the value of f(14) using the above function.

Show that if A and B are sets with the same cardinality, then |A|<=|B| and |B|<=|A|

Prove that if n is an odd positive integer, then n^2 ≡ 1 (mod 8).