State Demorgan’s law. Verify one of them using truth table.
Answer:
There are two Demorgan’s law:
(i) (A.B)’ = A’ + B’
(ii) (A+B)’ = A’.B’
Proof:
(i)
|
A |
B |
A’ |
B’ |
A.B |
(A.B)’ |
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 |
(ii)
|
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 |