Given the implication, If $p$, then $q$, translates to $p \implies q$. It has the truth table that makes the meaning/interpretation as: $\lnot p \lor q.$
If need find the converse, then it is given by: If $q$, then $p$, that translates to $q \implies p$, and interpretation in logic as $\lnot q\lor p.$
If need find the inverse, then it is given by: If not $p$, then not $q$, that translates to $\lnot p \implies \lnot q$, and interpretation in logic as $\lnot q \lor p.$
So, the converse and inverse are logically equivalent. Then, is it an ease in constructing proofs that necessitates the need for both converse & inverse to be used?
For example, if given that: if $p_1 \wedge p_2$, then $q$, then for finding the converse need prove:
if $q$, then $p_1 \wedge p_2$;
while the equivalent logic is provided by proving inverse as:
if $\lnot(p_1 \wedge p_2)$, then $\lnot q.$
"if $q$, then $p_1 \wedge p_2$" $\equiv$ "if $\lnot(p_1 \wedge p_2)$, then $\lnot q$".
So, is it the ease which allows us to choose which form to take for taking converse, to check if inverse is possible or not. If yes, then in which situations (like, possibly for compound propositions), this ease is helpful.