Question

Simplify to reach 3 product terms each of 2 variables only. X’YZ + XYZ’ + XYZ + XY’Z

Answer 1

The given expression is:

X’YZ + XYZ’ + XYZ + XY’Z

The solution of above expression is given below:

= X’YZ + XYZ’ + XZ(Y + Y’)

= X’YZ + XYZ’ + XZ    (By using complement law, X + X' = 1)

= X’YZ + X(YZ’ + Z)

= X’YZ + X( Z + Z’Y)

= X’YZ + X( Z + Y)   (Because X + X'Y = X + Y)

= X’YZ + XZ + XY

= Z(X’Y + X) + XY

= Z(X + X’Y) + XY

= Z(X + Y) + XY   (Because X + X'Y = X + Y)

= ZX + ZY + XY

= XY + ZY + ZX

= XY + YZ + ZX

This result has three product term and each of two variable only.