Absorption law states that
A + A . B = A and A . (A + B) = A
Proof:
The Truth table of the expression A + A .
B = A is as follows.
| A |
B |
A.B |
A + A.B |
| 0 |
0 |
0 |
0 |
| 0 |
1 |
0 |
0 |
| 1 |
0 |
0 |
1 |
| 1 |
1 |
1 |
1 |
Here both columns A and A + A . B are identical. Hence proved.
For A . (A + B) = A, the truth table is as follows:
| A |
B |
A+B |
A .( A+B) |
| 0 |
0 |
0 |
0 |
| 0 |
1 |
0 |
0 |
| 1 |
0 |
0 |
1 |
| 1 |
1 |
1 |
1 |
Both columns A & A . (A + B) are identical. Hence proved
