Q. Let ๐บ be an arbitrary group. Consider the following relations on ๐บ:
๐ 1: โ๐, ๐ โ ๐บ, ๐ ๐ 1๐ if and only if โ๐ โ ๐บ such that ๐ = ๐โ1๐๐
๐ 2: โ๐, ๐ โ ๐บ, ๐ ๐ 2๐ if and only if ๐ = ๐โ1
Which of the above is/are equivalence relation/relations?
(A) ๐ 1 and ๐ 2
(B) ๐ 1 only
(C) ๐ 2 only
(D) Neither ๐ 1 nor ๐ 2
Ans: ๐ 1 only
Solution:
![Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]](https://www.gkseries.com/blog/wp-content/uploads/2023/10/Determine-the-correctness-or-otherwise-of-the-following-Assertion-A-and-the-Reason-R.jpg)
