$4.($a$)$ The Absorption Law is the logical equivalence p $($p $$ q$)$ p$.$ Explain in words why it is true by

first assuming that p is true and explaining why p$($p$$q$)$ must be true and then assuming that p

is false and explaining why p$($p$$q$)$ must be false. Why does this prove the logical equivalence?

$($b$)$ Use Laws of Logic and Known Logical Equivalences to prove that $($r $->$ q$)($q $$p$)$ is logically

equivalent to $($q $$ p$).$ You are allowed to use the Absorption Law defined in part $($a$).$