Class JEE Mathematics Sets, Relations, and Functions Q #1028
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4 Marks 2024 JEE Main 2024 (Online) 27th January Morning Shift MCQ SINGLE
Let $S = {1, 2, 3, …, 10}$. Suppose $M$ is the set of all the subsets of $S$, then the relation $R = {(A, B) : A ∩ B ≠ 𝜙; A, B ∈ M}$ is :
(A) symmetric only
(B) reflexive only
(C) symmetric and reflexive only
(D) symmetric and transitive only
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Correct Answer: A
Explanation
Let $S = {1, 2, 3, …, 10}$. $R = {(A, B): A∩B ≠ 𝜙; A, B∈ M}$.
For Reflexive, $M$ is subset of 'S'. So $𝜙 ∈ M$ for $𝜙 ∩ 𝜙 = 𝜙 ⇒$ but relation is $A ∩ B ≠ 𝜙$. So it is not reflexive.
For symmetric, $A R B ⇒ A ∩ B ≠ 𝜙, ⇒ B R A ⇒ B ∩ A ≠ 𝜙$, So it is symmetric.
For transitive, If $A = {(1, 2), (2, 3)}, B = {(2, 3), (3, 4)}, C = {(3, 4), (5, 6)}$. $A R B$ & $B R C$ but $A$ does not relate to $C$. So it not transitive.

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