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Verify if the following proposition is valid using the truth table:
Verify if the following proposition is valid using the truth table:
$A \Rightarrow ( B \land C ) = ( A \Rightarrow B ) \land ( B \Rightarrow C )$
Answer
Answer
AITruth table:
The LHS and RHS columns agree in every row except A=0, B=1, C=0, where LHS=1 but RHS=0. Since the two sides are not identical for every combination of A, B, C, the given proposition is NOT VALID (it is not a tautology).
| A | B | C | B.C | LHS: A=>(B.C) | A=>B | B=>C | RHS: (A=>B).(B=>C) |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
From ISC 2024 Specimen Computer Science Paper 1, question 5(ii).