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Using the truth table, state whether the following proposition is a tautology, contingency or a…
Using the truth table, state whether the following proposition is a tautology, contingency or a contradiction:
$\sim( A \land B ) \lor ( \sim A \implies B )$
Answer
Answer
AI$\sim(A \land B) \lor (\sim A \implies B)$
Truth table (verified with the boolean tool):
The final column is 1 (True) for every combination of A and B. Hence the given proposition is a Tautology.
| A | B | A.B | (A.B)' | A' | A'=>B | (A.B)'+(A'=>B) |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 1 | 1 |
From ISC 2018 Computer Science Paper 1, question 5(b).