You may use a calculator on this quiz. If you get stuck on a question, move on to the next. If you have time left over at the end of the quiz, check your work.

- Shown below is the truth table for the statement (¬p) ∨ (¬q).

a) (15 pts) Construct the truth table for ¬(p ∨ q).**p****q****¬p****¬q****(¬p) ∨ (¬q)**T T F F F T F F T T F T T F T F F T T T b) (10 pts) Is ¬(p ∨ q) equivalent to (¬p) ∨ (¬q)? Explain.

- (25 pts) Suppose P(x) represents the propositional function x² >
x+1 and the domain of discourse D is all positive numbers. Is
∀x P(x) a true or false statement? Explain.
- If A = {a, b, c, d} and B = {c, d, e, f}

a) (15 pts) What is A ∩ B?b) (10 pts) What is A - B?

- To prove the propositional function S(n): 1 + 2 + 3 + ... + (n-1)
+ n = n*(n+1)/2 by induction, we first proved S(1).

a) (10 pts) What is S(1)?We next assumed that 1 + 2 + 3 + ... + (k-1) + k = k*(k+1)/2 (statement S(k)) and used this assumption to prove S(k+1).

b) (15 pts) What is S(k+1)?