Let $G$ be an arbitrary group. Consider the following relations on $G$: $$R_1: \forall a, b \in G, \; a \, R_1 \, b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$$ $$R_2: \forall a, b \in G, \; a \, R_2 \, b \text{ if and only if } a = b^{-1}$$ Which of the above is/are equivalence relation/relations?

Let G be an arbitrary group. Consider the following relations on G: R1: a, b G, \; a \, R1 \, b if and only if g G such that a = g-1bg R2: a, b G, \; a \, R2 \, b if and only if a = b-1 Which of the above is/are equivalence relation/relations?

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