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Question
Which of the following statement pattern is a tautology?
Options
`p ∨ (q rightarrow p)`
`∼q rightarrow ∼p`
`(q rightarrow p) ∨ (∼p leftrightarrow q)`
`p ∧ ∼p`
MCQ
Solution
`bb((q rightarrow p) ∨ (∼p leftrightarrow q))`
Explanation:
The truth table is given below:
| `bb(p)` | `bb(q)` | `bb(∼p)` | `bb(∼q)` | `bb(∼p leftrightarrow q)` | `bb(q rightarrow p)` | `bb(∼q rightarrow ∼p)` | `bb(p ∨ (q rightarrow p))` | `bb(p ∧ ∼p)` | `bb((q rightarrow p) ∨ (∼p leftrightarrow q))` |
| T | T | F | F | F | T | F | T | F | T |
| T | F | F | T | T | T | F | T | F | T |
| F | T | T | F | T | F | T | T | F | T |
| F | F | T | T | F | T | T | F | F | T |
Hence `(q rightarrow p) ∨ (∼p rightarrow q)` is a tautology.
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Tautology, Contradiction, and Contingency
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