Question:
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
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
Updated On: Apr 16, 2026
- \(\begin{array}{l} \left(\left(\sim q\right) \wedge \left(r\vee s\right)\right) \Rightarrow p \end{array}\)
- \( \left(q\wedge \left(r\vee s \right)\right) \Rightarrow p\)
- \(p\Rightarrow \left(q\wedge \left(r\vee s\right)\right)\)
- \(p\Rightarrow \left(\sim q \right) \wedge \left(r\vee s\right)\)
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The Correct Option is D
Solution and Explanation
p : Ramesh listens to music
q : Ramesh is out of his village
r : It is Sunday
s : It is Saturday
p→q conveys the same p only if q
Statement “Ramesh listens to music only if he is in his village and it is Sunday or Saturday”
\(p ⇒ ((~ q) ∧ (r∨s))\)
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Concepts Used:
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Mathematical reasoning or the principle of mathematical reasoning is a part of mathematics where we decide the truth values of the given statements. These reasoning statements are common in most competitive exams like JEE and the questions are extremely easy and fun to solve.
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Mathematically, reasoning can be of two major types such as:
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- Deductive Reasoning - The principle is the opposite of the principle of induction. Contrary to inductive reasoning, in deductive reasoning, we apply the rules of a general case to a provided statement and make it true for particular statements. The principle of mathematical induction utilizes the concept of deductive reasoning.