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, q = false:

- p ∧ q = true ∧ false = false
- p ∨ q = true ∨ false = true
- p → q = true → false = false
- q → p = false → true = true
- p ↔ q = (true iff false) = false
- q ↔ p = (false iff true) = false

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