JEE Main20231 Feb 2023Evening ShiftMathematicsMathematical ReasoningActual
Which of the following statements is a tautology?
Options
- Ap → p ∧ p → q
- Bp ∧ q → ~ p → q
- Cp ∧ p → q → ~ q
- Dp ∨ p ∧ q
Correct answer
B. p ∧ q → ~ p → q
Step-by-step solution
We know, A → B ≡ ~ A ∨ B Now solving all options one by one we get, A   p → p ∧ p → q ≡ ~ p ∨ p ∧ ~ p ∨ q ≡ ~ p ∨ f ∨ p ∧ q ≡ ~ p   ∨ p ∧ q ≡ ~ p ∨ p ∧ ~ p ∨ q ≡ ~ p   ∨   q Which is not a tautology B   p ∧ q → ~ p → q ≡ ~ p ∧ q ∨ p ∨ q ≡ ~ p ∨ ~ q ∨ p ∨ q ≡ ~ p ∨ p ∨ ~ q