Simplify the given expressions using Boolean postulates
XY + X‾Z‾ + XY‾Z (XY + Z)
Ans. XY + X‾Z‾ + XY‾Z (XY + Z)
= XY + X‾Z‾ + XY‾Z (XY + Z)
= XY + X‾Z‾ + XXYY‾Z + XY‾ZZ
= XY + X‾Z‾ + XYZ (As YY‾ = 0 and ZZ = Z)
= XY + X‾ + Z‾ + XY‾Z (As X‾Z‾ = X‾ + Z‾)
= X‾ + XY + Z‾ + XY‾Z
= X‾ + X (Y + Y‾Z) + Z‾
= X‾ + X (Y +Z) + Z‾ (As Y + Y‾Z = Y+Z)
= X‾ + X Y (Z+ Z‾ ) + XZ + Z‾ (As Z+ Z‾ =1)
= X‾ + X Y Z + XYZ‾ + XZ + Z‾
= X‾ + XZ (1+ Y) + Z‾ (1+XY)
= X‾ + XZ + Z‾ (As 1+ Y = 1 and 1+XY = 1)
= X‾ + XZ) + Z‾
=(X‾ + Z) + Z‾ (As X‾ + XZ = X‾ + Z‾
= X‾ +( Z + Z‾)
= X‾ +1 (As Z + Z‾ = 1)
=1 (As X‾ +1 = 1)