Demorgan’s first theorem states that (A + B)’ = A’ . B’
ie. the complement of sum of two variables equals product of their complements,
The second theorem states that (A . B)’ = A’ + B’
ie. The complement of the product of two variables equals the sum of the complement of that variables.
Proof:
Truth table of first one is as follows:
| A |
B |
A +B |
(A + B)’ |
A’ |
B’ |
A’ . B’ |
| 0 |
0 |
0 |
1 |
1 |
1 |
1 |
| 0 |
1 |
1 |
0 |
1 |
0 |
0 |
| 1 |
0 |
1 |
0 |
0 |
1 |
0 |
| 1 |
1 |
1 |
0 |
0 |
0 |
0 |
From the truth table the columns of both (A + B)’ and A’ . B’ are identical. Hence proved.
