alleryStart learning →The CONTRAPOSITIVE of $P \to Q$ is
A$Q \to P$ (converse)
B$\neg P \to \neg Q$ (inverse)
C$\neg Q \to \neg P$
D$P \land \neg Q$
Answer & Solution
Correct answer: C. $\neg Q \to \neg P$
1. CONTRAPOSITIVE: negate and reverse both sides. $P \to Q$ becomes $\neg Q \to \neg P$.
2. CRUCIAL: an implication and its contrapositive are LOGICALLY EQUIVALENT — they have the same truth table.
3. Example: 'If it rains, the street is wet' has contrapositive 'If the street is not wet, it did not rain'.
4. Option A is the CONVERSE (not logically equivalent). Option B is the INVERSE (also not equivalent). Option D is the NEGATION of the implication.
_Source: Oscar Levin, "Discrete Mathematics: An Open Introduction", §0.2 (Implications, Converse, Inverse, Contrapositive)._
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