Question

Suppose statement p is true but statement q is false. Which of these compound statements are true? Check all that apply.

p ∧ q
p ∨ q
p → q
q → p
p ↔ q
q ↔ p

Answer 1

Given p = true and q = false:

- p ∧ q: false (both must be true)
- p ∨ q: true (at least one — p — is true)
- p → q: false (true implies false is false)
- q → p: true (false implies true is true — implication with false antecedent is true)
- p ↔ q: false (they differ)
- q ↔ p: false (same as p ↔ q)

So the true compound statements are: p ∨ q and q → p.