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By using truth table, verify if the following proposition is valid or not.
By using truth table, verify if the following proposition is valid or not.
$(\sim X \Rightarrow Y) \wedge X = (X \wedge \sim Y) \vee (X \wedge Y)$
Answer
Answer
AITruth table:
The LHS column $(\sim X \Rightarrow Y) \wedge X$ and the RHS column $(X \wedge \sim Y) \vee (X \wedge Y)$ are identical for every row (0,0,1,1). Hence the given proposition is VALID (the two sides are logically equivalent).
| X | Y | X' | X'=>Y | (X'=>Y).X | X.~Y | X.Y | (X.~Y)+(X.Y) |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
From ISC 2025 Computer Science Paper 1, question 5(ii).