- 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)?
Bonus: (5 pts) As described in the problem above, assume S(k) is true and use
this to prove S(k+1).