$3.$ Use Boolean theorems to prove the following identities:

$($a$)$ A$($A$+$B$)=$ A$$B

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

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

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