Which one of the following is the contrapositive, in words, of the conditional logic statement p → q?
Understand the Problem
The question asks for the contrapositive of the conditional statement p → q, where p and q are defined in terms of the divisibility of a positive integer n. The contrapositive involves negating both the hypothesis and conclusion of the original statement and flipping them.
Answer
If not q, then not p.
The contrapositive of the conditional logic statement 'if p, then q' is 'if not q, then not p.'
Answer for screen readers
The contrapositive of the conditional logic statement 'if p, then q' is 'if not q, then not p.'
More Information
In logical equivalence, a contrapositive is always logically equivalent to the original conditional statement. This means that both the contrapositive and the original statement will always have the same truth value.
Tips
A common mistake is to confuse the contrapositive with the converse or the inverse. Remember: the contrapositive switches both the order and the negation of the hypothesis and conclusion.
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