# The Contrapositive

Today’s lesson comes from formal logic: the contrapositive. The contrapositive is the a reversal of an if-then statement, that is also true. In fact, it is the only construction that is always true. It is constructed by reversing the two items in the if-then statement and taking the opposite of both.

For example, a person might say, “if you jump off a bridge, then you will die.” The contrapositive of this statement is, “if you are alive, then you did not jump off a bridge.”

If the original statement is true, the contrapositive is true, and if the contrapositive is false, then the original statement is false. NB: Did you notice that I used the contrapositive here too?

Formally, the contrapositive is written as:

Original: $A \rightarrow B$

Contrapositive: $-B \rightarrow -A$

Quiz: For the statement, “If you have read this far, then you have reached the end of the post,” what is the contrapositive?

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