Let X be a non-void set. If rho_1 and rho_2 a | vedclass

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(B) relation $\rho$ on a set $X$ is transitive if $(a, b) \in \rho$ and $(b, c) \in \rho$ implies $(a, c) \in \rho$. Consider the intersection of two

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$\rho_1 \cap \rho_2$ is a transitive relation

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(B) relation $\rho$ on a set $X$ is transitive if $(a, b) \in \rho$ and $(b, c) \in \rho$ implies $(a, c) \in \rho$. Consider the intersection of two transitive relations $\rho_1$ and $\rho_2$. Let $(a, b) \in \rho_1 \cap \rho_2$ and $(b, c) \in \rho_1 \cap \rho_2$. This implies $(a, b) \in \rho_1$ and $(b, c) \in \rho_1$, and since $\rho_1$ is transitive, $(a, c) \in \rho_1$. Similarly, $(a, b) \in \rho_2$ and $(b, c) \in \rho_2$, and since $\rho_2$ is transitive, $(a, c) \in \rho_2$. Therefore, $(a, c) \in \rho_1 \cap \rho_2$. Thus, the intersection of two transitive relations is always a transitive relation.

Let $X$ be a non-void set. If $\rho_1$ and $\rho_2$ are transitive relations on $X$, then which of the following is true?

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