Question

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 1

Answer: (B)

Union of two transitive may or may not be transitive