$9.(12$pts$)$ Determine if the following are tautologies, contradictions or contingencies by using logical equivalences. State the rules of logic that you use in each step. Note, you cannot use truth tables to justify your answers. $($a$)($p $($p $->$ q$))->$ q $($b$)(($p $$ q $$ r$)$ r$)($ r $($q $$ p$)$ r$)($c$)($a $->$ b$)(($a $$ b$)->$ c$)$