If P ∨ Q is false, what can be said about P and Q?

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Multiple Choice

If P ∨ Q is false, what can be said about P and Q?

Explanation:
Disjunction means “P or Q” is true if at least one of P or Q is true. It is false only when both P and Q are false. So if P ∨ Q is false, both P and Q must be false. If either one were true, the statement “P or Q” would be true. A quick intuitive example: if P says “it is raining” and Q says “it is sunny,” then “it is raining or it is sunny” is false only when neither condition holds, i.e., both P and Q are false.

Disjunction means “P or Q” is true if at least one of P or Q is true. It is false only when both P and Q are false. So if P ∨ Q is false, both P and Q must be false. If either one were true, the statement “P or Q” would be true. A quick intuitive example: if P says “it is raining” and Q says “it is sunny,” then “it is raining or it is sunny” is false only when neither condition holds, i.e., both P and Q are false.

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