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JEE Main 202228 JulyEvening Shift
Exam
JEE Main
Year
2022
Date
28 July
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2022 · 28 July · Evening Shift · Mathematics · Mathematical Reasoning

Let p: Ramesh listens to music. q: Ramesh is out of his village r:...

Let
p:p: Ramesh listens to music.
q:q: Ramesh is out of his village
r:r: It is Sunday
s: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\left(\left(~ q\right) ∧ \left(r ∨ s\right)\right) ⇒ p
  2. B(q∧(r∨s))⇒p\left(q ∧ \left(r ∨ s\right)\right) ⇒ p
  3. Cp⇒(q∧(r∨s))p ⇒ \left(q ∧ \left(r ∨ s\right)\right)
  4. Dp⇒(( q)∧(r∨s))p ⇒ \left(( ~ q ) ∧ \left(r ∨ s\right)\right)

Correct answer

D. p⇒(( q)∧(r∨s))p ⇒ \left(( ~ q ) ∧ \left(r ∨ s\right)\right)

Step-by-step solution

Given,
p:p: Ramesh listens to music.
q:q: Ramesh is out of his village
r:r: It is Sunday
s: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≡p ≡ Ramesh listens to music

 q≡~ q ≡ He is in village.

r∨s≡r ∨ s ≡ Saturday or Sunday

So, on combining all statement we get,

p⇒(( q)∧(r∨s))p ⇒ \left(\left(~ q\right) ∧ \left(r ∨ s\right)\right)

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