Question

The truth table represents statements p, q, and r.

p q r
A T T T
B T T F
C T F T
D T F F
E F T T
F F T F
G F F T
H F F F
Which statement is true for rows A, C, and E?

r → (p ∧ q)
r → (p ∨ q)
(q ∧ r) → p
(q ∨ r) → p

Answer 1

r → (p ∨ q)

Reason: In A, C, E we have r = T and p ∨ q = T, so r → (p ∨ q) = T → T = T in each. The other formulas fail on at least one of those rows (e.g. r → (p ∧ q) fails in C and E; (q ∧ r) → p and (q ∨ r) → p fail in E).