Answer
The converse of p $\rightarrow$ q is q $\rightarrow$ p.
The inverse of p $\rightarrow$ q is ~p $\rightarrow$ ~q.
The truth table shows the converse and inverse of a conditional statement have the same truth values, so they are logically equivalent.
Additionally, the converse of a conditional statement is the contrapositive of the inverse of the conditional statement. Problem 26 proved a conditional statement and its contrapositive are logically equivalent, so since the converse and inverse are contrapositives of each other, they are logically equivalent.
Work Step by Step
To evaluate the if/then statements, recall by the definition of a conditional statement, when the if element is T and the then element is F, the statement is F. In all other cases the statement is T. Two statements are only logically equivalent if, and only if, they have identical truth values for each possible substitution of statements for their statement variables.
