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Under what condition is the material implication P → Q fa... | QuestionStock

Representative image for question: Under what condition is the material implication P → Q false in classical propositional logic?

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Logic

Under what condition is the material implication P → Q false in classical propositional logic?

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Under what condition is the material implication P → Q false in classical propositional logic?

Options:

When both P and Q are false
When P is false and Q is true
When P is true and Q is false
When both P and Q are true

Correct answer: When P is true and Q is false

Explanation: Material implication P→Q is false exactly in the single truth-table case where P is true and Q is false; out of four rows, only T→F yields false.

Created 2026-03-10T18:53:24.083Z. Updated 2026-03-10T18:53:24.083Z.