JEE Mains · Maths · STD 12 - 1. relation and function
Let \(S=\{1,2,3, \ldots, 10\}\). Suppose \(M\) is the set of all the subsets of \(S\), then the relation \(R=\{(A, B): A \cap B \neq \phi ; A, B \in M\}\) is :
- A symmetric and reflexive only
- B reflexive only
- C symmetric and transitive only
- D symmetric only
Answer & Solution
Correct Answer
(D) symmetric only
Step-by-step Solution
Detailed explanation
Let \(S=\{1,2,3, \ldots, 10\}\) \(R=\{(A, B): A \cap B \neq \phi ; A, B \in M\}\) For Reflexive, \(M\) is subset of ' \(S\) ' So \(\phi \in \mathrm{M}\) for \(\phi \cap \phi=\phi\) \(\Rightarrow\) but relation is \(\mathrm{A} \cap \mathrm{B} \neq \phi\) So it is not reflexive.…
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