sing logical equivalences, determine if the following are tautologies, contradictions or contingencies.

State the rules of logic that you use in each step. Do not apply more than two laws per step. Note that you

cannot use truth tables to justify your answers.

$($a$)($a $$b$)($a $->$ b$)$

$($b$)($p $$ q$)($p $$ q$)$p

$($c$)(($p $->$ q$)$ p$)->($q $$ q$)$

$($d$)($a $->$b$)(($a $$ b$)->$c$)$