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JEE Main20236 Apr 2023Morning ShiftMathematicsMathematical ReasoningActual

Statement ( P ⇒ Q ) ∧ ( R ⇒ Q ) is logically equivalent to

Options

  1. AP ⇒ R ∨ Q ⇒ R
  2. BP ∧ R ⇒ Q
  3. CP ⇒ R ∧ Q ⇒ R
  4. DP ∨ R ⇒ Q

Correct answer

D. P ∨ R ⇒ Q

Step-by-step solution

Given that ( P ⇒ Q ) ∧ ( R ⇒ Q ) We know that P ⇒ Q ≡ ~ P ∨ Q ⇒ ~ P ∨ Q ∧ ~ R ∨ Q ⇒ ~ P ∧ ~ R ∨ Q ⇒ ~ P ∨ R ∨ Q ⇒ P ∨ R ⇒ Q Hence this is the correct option.

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