Computer Science
Prove the following relation:
(P ^ Q) v (P ^ ~Q) = P
Boolean Algebra
ICSE 2018
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Answer
| P | Q | ~Q | P^Q | P^~Q | (P^Q)v(P^~Q) |
|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 | 0 | 1 |
The columns of P and (P ^ Q) v (P ^ ~Q) have the same entries. Hence, the relation is proved.
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