(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)