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Let n be a fixed positive integer. Defin...

Let `n` be a fixed positive integer. Define a relation `R` on `Z` as follows: `(a ,\ b) in RhArra-b` is divisible by `ndot` Show that `R` is an equivalence relation on `Zdot`

A

Symmetric only

B

Reflexive and symmetric only

C

Symmetric and transitive only

D

Equivalence

Text Solution

Verified by Experts

The correct Answer is:
D
Let 'n' be a fixed …………..
If `(a-b)` is divisible by n
then `(a-a)` is also divisible by 'n'
i.e. `a R a`
similarly `a R b hArr b R a`
If `a R b and b R c, then a R c`
i.e. `(a-b)= lambda n and (b-c) = kn`
then `(a-c)= mu n`
`:.` Equivalence relation
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