JEE Main20208 Jan 2020Evening ShiftMathematicsMathematical ReasoningActual
Which of the following statement is a tautology?
Options
- Ap ∨ ~ q → p ∧ q
- B~ p ∧ ~ q → p ∨ q
- C~ p ∨ ~ q → p ∧ q
- D~ p ∨ ~ q → p ∨ q
Correct answer
D. ~ p ∨ ~ q → p ∨ q
Step-by-step solution
From De Morgan's Law, ~ p ∨ q = ~ p ∧ ~ q p → q = ~ p ∧ ~ q ~ p ∧ q → p ∨ q = ~ ~ p ∧ q ∧ ~ p ∧ ~ q = ~ ~ p ∧ f = ~ f = t , where f is contradiction and t is tautology.