## 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 Hence here the converse is: If all troops were withdrawn, then the president is telling the truth. The inverse: If the president is not telling the truth, then some troops were not withdrawn. The contrapositive: If some troops were not withdrawn, then the president was not telling the truth.