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Using a truth table, state whether the following proposition is a Tautology, Contradiction or…
Using a truth table, state whether the following proposition is a Tautology, Contradiction or Contingency:
$\sim(P =>Q) <=> (\sim P \lor Q)$
Answer
Answer
AITruth table (verified with the boolean tool):
The final column is 0 (False) for every combination of P and Q. Therefore the given proposition is a Contradiction.
| P | Q | P=>Q | ~(P=>Q) | ~P | ~P v Q | ~(P=>Q) <=> (~P v Q) |
|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0 | 1 | 0 |
From ISC 2019 Computer Science Paper 1, question 5(c).