JEE Main 20208 JanuaryMorning Shift
- Exam
- JEE Main
- Year
- 2020
- Date
- 8 January
- Shift
- Morning Shift
- Subject
- Mathematics
- Chapter
- Mathematical Reasoning
JEE Main 2020 · 8 January · Morning Shift · Mathematics · Mathematical Reasoning
Which one of the following is a tautology?
Which one of the following is a tautology?
Options
- A(p∧(p→q))→q
- Bq→(p∧(p→q))
- Cp∧(p∨q)
- Dp∨(p∧q)
Correct answer
A. (p∧(p→q))→q
Step-by-step solution
| p | q | p→q | p∧(p∧→q) | \left(p ∧ \left(p \to q\right)\right) \to q</th><th>q \to \left(p ∧ \left(p \to q\right)\right)</th><th>p ∧ q</th><th>p ∨ \left(p ∧ q\right)</th><th>p ∨ q</th><th>p ∧ \left(p ∨ q\right)</th></tr></thead><tbody><tr><td>T</td><td>T</td><td>T</td><td>T</td><td>T</td><td>T</td><td>T</td><td>T</td><td>T</td><td>T</td></tr><tr><td>T</td><td>F</td><td>F</td><td>F</td><td>T</td><td>T</td><td>F</td><td>T</td><td>T</td><td>T</td></tr><tr><td>F</td><td>T</td><td>T</td><td>F</td><td>T</td><td>F</td><td>F</td><td>F</td><td>T</td><td>F</td></tr><tr><td>F</td><td>F</td><td>T</td><td>F</td><td>T</td><td>T</td><td>F</td><td>F</td><td>F</td><td>F |
