The contrapositive of 'If p, then q' is which?

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Multiple Choice

The contrapositive of 'If p, then q' is which?

The idea being tested is that a conditional statement is logically equivalent to its contrapositive. For a statement like “If p, then q,” the contrapositive is “If not q, then not p.” This works because if p being true guarantees q, then whenever q is false, p cannot be true; otherwise q would be true when p is true. So the only way for q to be false is for p to also be false, which is exactly what “If not q, then not p” asserts. Example: If it is raining, the streets are wet. The contrapositive is: if the streets are not wet, it is not raining. Note that the inverse (if not p, then not q) and the converse (if q, then p) are different statements and don’t necessarily share the same truth value as the original.

The idea being tested is that a conditional statement is logically equivalent to its contrapositive. For a statement like “If p, then q,” the contrapositive is “If not q, then not p.” This works because if p being true guarantees q, then whenever q is false, p cannot be true; otherwise q would be true when p is true. So the only way for q to be false is for p to also be false, which is exactly what “If not q, then not p” asserts.

Example: If it is raining, the streets are wet. The contrapositive is: if the streets are not wet, it is not raining.

Note that the inverse (if not p, then not q) and the converse (if q, then p) are different statements and don’t necessarily share the same truth value as the original.

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