Prove the validity of the following statement using the laws of Boolean Algebra. For each step of the

proof, identify which law was used.

$($X $+$ Y $)$X$$Y $=$ X$$Y $$

X$$Y $+($X $+$ Y $)$Z $=$ X$$Y $+$ Z

A$$C $+$ BC $+$ AB $=$ A$$C $+$ AB

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