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JEE Main202228 Jul 2022Evening ShiftMathematicsMathematical ReasoningActual

Let p : Ramesh listens to music. q : Ramesh is out of his village r : It is Sunday s : It is Saturday Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as

Options

  1. A~ q ∧ r ∨ s ⇒ p
  2. Bq ∧ r ∨ s ⇒ p
  3. Cp ⇒ q ∧ r ∨ s
  4. Dp ⇒ ( ~ q ) ∧ r ∨ s

Correct answer

D. p ⇒ ( ~ q ) ∧ r ∨ s

Step-by-step solution

Given, p : Ramesh listens to music. q : Ramesh is out of his village r : It is Sunday s : It is Saturday Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as Now on breaking each statement and combining them we get, p ≡ Ramesh listens to music ~ q ≡ He is in village. r ∨ s ≡ Saturday or Sunday So, on combining all statement we get, p ⇒ ~ q ∧ r ∨ s

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