JEE Main202228 Jun 2022Morning ShiftMathematicsMathematical ReasoningActual
Let p , q , r be three logical statements. Consider the compound statements S 1 : ~ p ∨ q ∨ ~ p ∨ r and S 2 : p → q ∨ r Then, which of the following is NOT true?
Options
- AIf S 2 is True, then S 1 is True
- BIf S 2 is False, then S 1 is False
- CIf S 2 is False, then S 1 is True
- DIf S 1 is False, then S 2 is False
Correct answer
C. If S 2 is False, then S 1 is True
Step-by-step solution
S 1 : ~ p ∨ q ∨ ~ p ∨ r ≡ ~ p ∨ q ∨ r S 2 : p → q ∨ r ≡ ~ p ∨ q ∨ r So S 1 is equivalent to S 2