Laws Of Boolean Algebra
The Laws Of Boolean Algebra is provided here.
OR
A + 0 = A
A + A’ = 1
A + B = B + A
A (B + C) = AB + AC
A + A = A
A + 1 = 1
A + AB = A
A + (B + C) = (A + B) + C
A” = A
AND
A . 1 = A
A . A’ = 0
A . B = BA
A + BC = (A + B) (A + C)
A . A = A
A . 0 = 0
A (A + B) = A , ( AA+ AB = A, A + AB = A)
A (BC) = (AB) C
Distributive Law:
A . (B + C) = (A . B) + (A . C)
A + (B . C) = (A + B) . (A + C)
Associative Law:
A + (B + C) = (A + B) + C
A . (B .C) = (A . B) . C
Demorgan’s Theorem:
1. (AB)’ = A’ + B’
The product of the compliment is equal to the sum of the compliments
Proof:
| A | B | A’ | B’ | (AB) | (AB)’ | A’ + B’ |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 0 | 0 |
2.(A + B)’ = A’ . B’
The sum of the compliment is equal to the product of the compliments.
Proof:
| A | B | A’ | B’ | (A + B) | (A + B)’ | A’. B’ |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 | 0 |