Warm up problem 19: logic

The contrapositive of a conditional statement is logically equivalent to the original statement but with the antecedent and consequent "flipped" and negated. Thus the contrapositive of $p \Longrightarrow q$ is ~ $q \Longrightarrow$ ~ $p$ .

The converse of a conditional statement involves a flip of the antecedent and consequent. Thus the converse of ~ $q \Longrightarrow$ ~ $p$ is ~ $p \Longrightarrow$ ~ $q$ .

Finally, the inverse of a conditional statement involves the negation of the antecedent and the consequent. Thus the inverse of ~ $p \Longrightarrow$ ~ $q$ is

~(~ $p) \Longrightarrow$ ~(~ $q)$ , which is the same as $\boxed{p \Longrightarrow q}$ .

The more things change, the more they stay the same ......

A simple way to look at this problem; Contra positive is the inverse and the converse. If you do the contra positive and then take the inverse and converse, the statement stays the same