## Thinking Mathematically (6th Edition)

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 I am in the South, then I am in Birmingham. The inverse: If I am not in Birmingham, then I am not in the South. The contrapositive: If I am not in the South, then I am not in Birmingham.