# Converse, Inverse, and Contrapositive

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In propositional logic, the terms converse, inverse, and contrapositive arise.

Symbolically, an implication statement takes the form p → q. In words, an example of such a statement might be, "If you are in Trenton, then you are in New Jersey." The converse, inverse, and contrapositive of that statement are as follows:
Converse Inverse q → p If you are in New Jersey, then you are in Trenton. ¬p → ¬q If you are not in Trenton, then you are not in New Jersey. ¬q → ¬p If you are not in New Jersey, then you are not in Trenton.

These statements are not all equivalent. Looking at the example statement, it's pretty easy to see that the converse and inverse aren't necessarily true if the original statement is true, for example. The original statement is equivalent to the contrapositive, while the converse is equivalent to the inverse.

Sources used (see bibliography page for titles corresponding to numbers): 35.