alleryStart learning →Which statements are LOGICALLY EQUIVALENT to $P \to Q$?
AConverse and inverse only
BContrapositive only
CConverse only
DAll three (converse, inverse, contrapositive)
Answer & Solution
Correct answer: B. Contrapositive only
1. Among the four related statements:
- Implication: $P \to Q$
- Converse: $Q \to P$
- Inverse: $\neg P \to \neg Q$
- Contrapositive: $\neg Q \to \neg P$
2. ONLY the implication and its CONTRAPOSITIVE share the same truth table.
3. CONVERSE and INVERSE share each other's truth table but are NOT equivalent to the original.
4. So the only equivalent statement is the contrapositive — option B.
_Source: Oscar Levin, "Discrete Mathematics: An Open Introduction", §0.2 (Logical equivalence)._
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