Question

Prove the complementarity law of Boolean algebra with the help of a truth table. Complementarity law state that

(a) X + X’ = 1

(b) X . X’= 0

Answer 1

(a) X + X’ = 1

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

| x | x' | R |
| 0 | 1 | 1 |
| 1 | 0 | 1 |

0 + 1 = 1 and 1 + 0 = 1

From truth table it is prove that X + X’ = 1

(b) X . X’= 0

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

| x | x' | R |
| 0 | 1 | 0 |
| 1 | 0 | 0 |

0 . 1 = 0 and 1 . 0 = 0

From truth table it is prove that X + X’ = 1 From truth table it is prove that X . X’= 0