Let 'n' be a fixed positive integer. A relation `R` on `I` is defined as `a R b hArr n|(a-b)`. Then `R` is `(n|(a-b)` means `(a-b)`, divisible by `n` with remainder 0)

Options

A. Symmetric only
B. Reflexive and symmetric only
C. Symmetric and transitive only
D. Equivalence

Answer

D

Explanation

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