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In the set Z of all integers, which of t...

In the set `Z` of all integers, which of the following relation `R` is not an equivalence relation? `x\ R\ y :` if `xlt=y` (b) `x\ R\ y :` if `x=y` (c) `x\ R\ y` : if `x-y` is an even integer (d) `x\ R\ y` : if `x=y` (mod 3)

A

`x R y : if x le y`

B

`x R y : if x = y`

C

`x R y : if x - y` is an even integer

D

`x R y : if x = y` (mod 3)

Text Solution

Verified by Experts

The correct Answer is:
A
If R is a relation defined by `x R y : if x le y`, then R is reflexive and transitive. But, it is not symmetric.
Here, R is not an equivalence relation.
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