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JEE Main202225 Jun 2022Morning ShiftMathematicsMathematical ReasoningActual

Consider the following two propositions : P 1 : ~ p → ~ q P 2 : p ∧ ~ q ∧ ~ p ∨ q If the proposition p → ~ p ∨ q is evaluated as FALSE, then

Options

  1. AP 1 is TRUE and P 2 is FALSE
  2. BP 1 is FALSE and P 2 is TRUE
  3. CBoth P 1 and P 2 are FALSE
  4. DBoth P 1 and P 2 are TRUE

Correct answer

C. Both P 1 and P 2 are FALSE

Step-by-step solution

p q ~ p ~ q ~ p ∨ q p → ~ p ∨ q p → ~ q ~ p → ~ q p ∧ ~ q p ∧ ~ q ∧ ~ p ∨ q T T F F T T F T F F T F F T F F T F T F F T T F T T T F F F F F T T T T T F F F p → ~ p ∨ q is F when p is true q is false from the table. Hence, P 1   &   P 2 both are false

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