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Question
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Options
p ∨ q
p ↔ q
∼p ∨ ∼q
q ∨ ∼p
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Solution
If p ∧ q is false and p ∨ q is true, then p ↔ q is not true.
Explanation:
Since p ∧ q = false, p and q cannot both be true. And since p ∨ q = true, at least one of them must be true. This ensures that p ↔ q (which requires p and q to have the same truth value) is not true.
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