Question $1(8$ Points$)$:

a$.$ Prove that the following logic statement is logically true using truth table:

b$.$ Prove that the following logic statement is logically true using proof by contradiction:

$(($p$^(^())$q$)->$r$)->(($p$->$r$)$vv$($q$->$r$))$

$($pls check image for clear understanding$)$