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Question: Answered & Verified by Expert
Let $\rho_{1}$ and $\rho_{2}$ be two equivalence relations defined on a non-void set $S$. Then
MathematicsSets and RelationsWBJEEWBJEE 2020
Options:
  • 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.
Solution:
2692 Upvotes Verified Answer
The correct answer is: $\rho_{1} \cap \rho_{2}$ is equivalence relation but $\rho_{1} \cup \rho_{2}$ is not so.
Hint:
Union of two transitive may or may not be transitive

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