Question

Let p: It is raining
Let q: Robert is laughing.

Assume p is true. Select two statements that must logically be true.

p ∨ q
p ∧ q
q → p
p → q
q ↔ p

Answer 1

Answers: p ∨ q and q → p.

Reason: If p is true then the disjunction p ∨ q is true (at least one disjunct is true). And the implication q → p is true whenever the consequent p is true (material implication). The other statements require q to be true or stronger equivalence, which we do not know.