$2.$ Use truth tables to prove the following Boolean theorems:

$($a$)$

A$($A$+$ B$)=$ A$,($b$)$

A$+$ B$$C $=($A$+$ B$)($A$+$C$).$

$($c$)$

A$+$ A$$ B $=$ A$,($d$)$

A$+($B $+$C$)=($A$+$ B$)+$C