WBJEE · Maths · Sets and Relations
Let \(\rho_{1}\) and \(\rho_{2}\) be two equivalence relations defined on a non-void set \(S\). Then
- A both \(\rho_{1} \cap \rho_{2}\) and \(\rho_{1} \cup \rho_{2}\) are equivalence relations
- B \(\rho_{1} \cap \rho_{2}\) is equivalence relation but \(\rho_{1} \cup \rho_{2}\) is not so.
- C \(\rho_{1} \cup \rho_{2}\) is equivalence relation but \(\rho_{1} \cap \rho_{2}\) is not so
- D neither \(\rho_{1} \cap \rho_{2}\) nor \(\rho_{1} \cup \rho_{2}\) is equivalence relation.
Answer & Solution
Correct Answer
(B) \(\rho_{1} \cap \rho_{2}\) is equivalence relation but \(\rho_{1} \cup \rho_{2}\) is not so.
Step-by-step Solution
Detailed explanation
Hint: Union of two transitive may or may not be transitive
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