Q. 17 Let G be an arbitrary group. Consider the following relations on G:
- R1: ∀a, b ∈ G, aR1b if and only if ∃g ∈ G such that a = g−1bg
- R2: ∀a, b ∈ G, aR2b if and only if a = b−1
Which of the above is/are equivalence relation/relations?
(A) R1 and R2
(B) R1 only
(C) R2 only
(D) Neither R1 nor R2
Answer: (B)
Explanation:
