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Verify if the following proposition is a Tautology, Contradiction or a Contingency, using a truth…
Verify if the following proposition is a Tautology, Contradiction or a Contingency, using a truth table.
$((A \Rightarrow B) \wedge (B \Rightarrow C)) \Rightarrow (A \Rightarrow C)$
Answer
Answer
AITruth table for ((A=>B).(B=>C)) => (A=>C):
The final column is 1 (True) for every combination of A, B and C. Therefore the given proposition is a Tautology.
| A | B | C | A=>B | B=>C | (A=>B).(B=>C) | A=>C | ((A=>B).(B=>C))=>(A=>C) |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
From ISC 2024 Computer Science Paper 1, question 4(ii).