Question

Give the truth table proof for distributive law of Boolean algebra. Distributive law state that

(a)  X(Y +Z) = XY + XZ

(b)  X + YZ = (X + Y)(X + Z)

Answer 1

(a) X(Y +Z) = XY + XZ 

To prove this law, we will make a following truth table :

 

(b)  X + YZ = (X + Y)(X + Z)From truth table it is prove that X(Y +Z) = XY + XZ

x	y	z	yz	x + yz	xz	x + y	x + z	(x + y)(x + z)
0	0	0	0	0	0	0	0	0
0	0	1	0	0	0	0	1	0
0	1	1	0	0	0	1	0	0
0	1	1	1	0	0	1	1	1
1	1	0	1	0	0	1	1	1
1	0	1	1	1	1	1	1	1
1	1	0	1	0	0	1	1	1
1	1	1	1	1	1	1	1	1

From truth table it is prove that X + YZ = (X + Y)(X + Z)