JEE Main · MathematicsHard
Let be the set of all subsets of . A relation is defined on by if and only if . Which of the following is true?
- A. is an equivalence relation
- B. is reflexive and symmetric
- C. is symmetric and transitive
- D. is only symmetric
Show correct answer & step-by-step solution
Correct answer: D — is only symmetric
Solution
The relation is symmetric because intersection is commutative. It is not reflexive because the empty set does not intersect itself, and it is not transitive as shown by counterexamples.
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