Computer Science
Verify the following using truth table:
(i) a.(a+b) = a
(ii) X.(Y+Z) = X.Y + X.Z
Answer
(i) a.(a+b) = a
Truth Table
| a | b | a + b | a.(a+b) | a |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 |
As columns "a.(a+b)" and "a" have same values, hence the expression is proved.
(ii) X.(Y+Z) = X.Y + X.Z
Truth Table
| X | Y | Z | Y+Z | X.(Y+Z) | X.Y | X.Z | X.Y+X.Z |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
As columns X.(Y+Z) and X.Y+X.Z have same values, hence the expression is proved.
