How many gates would be required to implement the following Boolean expression after simplification? XY + X(X + Z) + Y(X + Z)

ANS:B - 2

Given:

XY+X(X+Z)+Y(X+Z)

= XY+XX+XZ+YX+YZ .......(By Using Distributed Law)
= XY+X+XZ+YX+YZ .......(Idempotent we substitute here :(XX=X) )
= X+XY+YX+XZ+YZ .......(Rearrange the equation for simple simplify )
= X+XY+XZ+YZ .....(By Using Commutative Law : ( XY=YX) due to we substitute here

XY n again its common so again use here Idempotent)
= X+XZ+YZ .......(By Using Absorption Law : X+XY=X )
= X+YZ .......( By Absorption Law)

X+YZ.