Hello, Suvadip!
This is a strange problem.
I would like to see the textbook solution.
The relation is defined by: .
How to show that is not an equivalence relation?
- - - - - - - - - - - - - - - - - - - - - - - - -
is definitely reflexive and symmetric.
How to prove that it is not transitive? .I don't know . . .
Note that:
Does and imply .Yes!
Raise [1] to the power
Raise [2] to the power
Equate [3] and [4]: .
Therefore, is transitive. . is an equivalence relation.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
One explanation . . .
We can find one such relation: .
The difficulty is finding the second relation: .
. . where
That strictly depends upon who you think is correct. Study this page.
There is no general agreement on that point. So you must go by whatever your textbook/lecturer says.
For me is not defined.