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Let Z be the set of all integers and R b...

Let `Z` be the set of all integers and `R` be the relation on `Z` defined as `R={(a, b); a,\ b\ in Z,` and `(a-b)` is divisible by `5}`. Prove that `R` is an equivalence relation.

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Here, `R = {(a,b):a,b in R and (a-b)` is divisible by `5}`
For all `a in R`,
`=> (a-a) =0` and `0` is divisible by `5`.
`:. R` is refexive.
Since in `R` for every `(a,b) in R`
`=> (a-b)` is divisible by `5`.
...
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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
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