Modus Tollens

“denying the consequent”

A valid deductive argument form in formal logic. If $P$ implies $Q$ ($P\to Q$) and $Q$ is false ($\neg Q$), then $P$ must be false ($\neg P$). It is an indirect proof method, where negating the consequent ($Q$) denies the antecedent ($P$).

• Premise 1: $P\to Q$ (If $P$, then $Q$)
• Premise 2: $\neg Q$ (Not Q)
• Conclusion: $\neg P$ (Therefore, not $P$)