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JEE Main202126 Aug 2021Evening ShiftMathematicsMathematical ReasoningActual

Consider the two statements : S 1 : ( p → q ) ∨ ( ~ q → p ) is a tautology. S 2 : ( p ∧ ~ q ) ∧ ( ~ p ∨ q ) is a fallacy. Then :

Options

  1. Aonly ( S 1 ) is true.
  2. Bboth ( S 1 ) and ( S 2 ) are false.
  3. Conly ( S 2 ) is true.
  4. Dboth ( S 1 ) and ( S 2 ) are true.

Correct answer

D. both ( S 1 ) and ( S 2 ) are true.

Step-by-step solution

p q ~ p ~ q p → q ~ q → p ( p → q ) ∨ ( ~ q → p ) p ∧ ~ q ~ p ∨ q ( p ∧ ~ q ) ∧ ( ~ p ∨ q ) T T F F T T T F T F T F F T F T T T F F F T T F T T T F T F F F T T T F T F T F From table ( p → q ) ∨ ( ~ q → p ) is tautology and ( p ∧ ~ q ) ∧ ( ~ p ∨ q ) is fallacy.

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