## Thinking Mathematically (6th Edition)

The sentence in "if...then" form is: If a person is a senator, then he or she is a politician. The contrapositive of $p\rightarrow q$ is $\sim q\rightarrow p$. The converse of $p\rightarrow q$ is $q \rightarrow p$. The inverse of $p\rightarrow q$ is $\sim p\rightarrow q$. Hence here the converse is: If a person is a politician, then he or she is a senator. The inverse: If a person is not a senator, then he or she is not a politician. The contrapositive: If a person is not a politician, then he or she is not a senator.