(1) Determine which of the following sentences are statements. What are the
truth values of those that are statements?
(a) 3>2.
(b) Is2>3?
(c) Every continuous function is differentiable. (d) x2 −5x+6 = 0.
(2) Use truth tables to prove the following equivalences:
1. (a) P∧ ¬P ≡ False
2. (b) P∨ (Q∧R) ≡ (P∨ Q) ∧ (P∨ R)
3. (c) (P→ Q) ∨ (Q→ P) ≡True
4. (d) (P→ (Q∨R)) ≡((P∧¬ Q)→R)
truth values of those that are statements?
(a) 3>2.
(b) Is2>3?
(c) Every continuous function is differentiable. (d) x2 −5x+6 = 0.
(2) Use truth tables to prove the following equivalences:
1. (a) P∧ ¬P ≡ False
2. (b) P∨ (Q∧R) ≡ (P∨ Q) ∧ (P∨ R)
3. (c) (P→ Q) ∨ (Q→ P) ≡True
4. (d) (P→ (Q∨R)) ≡((P∧¬ Q)→R)
