JEE Main20202 Sep 2020Evening ShiftMathematicsMathematical ReasoningActual
Which of the following is a tautology?
Options
- A~ p ∧ p ∨ q → q
- Bq → p ∨ ~ p → q
- C~ q ∨ p ∧ q → q
- Dp → q ∧ q → p
Correct answer
A. ~ p ∧ p ∨ q → q
Step-by-step solution
A ~ p ∧ p ∨ q → q ~ p ∧ p ∨ ~ p ∧ q → q c ∨ ~ p ∧ q → q (where c is contradiction) ~ p ∧ q → q ~ ~ p ∧ q ∨ q = p ∨ ~ q ∨ q = p ∨ t = t C ~ q ∨ p ∧ q → q = ~ q ∨ p ∧ ~ q ∨ q → q = ~ q ∨ p → q = q ∧ ~ p ∨ q = q = q B and D p q p → q q → p ~ p → q ( p → q ) ∧ ( q → p ) ( q → p ) ∨ ~ ( p → q ) T T T T