Match the type of the proof $($a$-$c$)$ to its logical format. In each case the theorem being proved is p$->$q

a$.$ Proof by contradiction

b$.$ Direct proof

c$.$ Proof by contrapositive

Assume p$.$ Follow a series of steps to conclude q$.$

Assume not q$.$ Follow a series of steps to conclude not p$.$

Assume p$^$ not q$.$ Follow a series of logical steps to conclude r$^$ not r for some proposition r$.$