If R and R^1 are equivalence relations on a s | vedclass

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(D) An equivalence relation must be reflexive, symmetric, and transitive. $1$. For $R^{-1}$: Since $R$ is reflexive, symmetric, and transitive, $R^{-1

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Both $R^{-1}$ and $R \cap R^1$

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(D) An equivalence relation must be reflexive, symmetric, and transitive. $1$. For $R^{-1}$: Since $R$ is reflexive, symmetric, and transitive, $R^{-1}$ is also reflexive, symmetric, and transitive. Thus, $R^{-1}$ is an equivalence relation. $2$. For $R \cap R^1$: The intersection of two equivalence relations is always an equivalence relation. $3$. For $R \cup R^1$: The union of two equivalence relations is not necessarily transitive, so it is not always an equivalence relation. Therefore, both $R^{-1}$ and $R \cap R^1$ are equivalence relations.

If $R$ and $R^1$ are equivalence relations on a set $A$, then which of the following is also an equivalence relation?

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