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In the set Z of integers define mRn if m...

In the set Z of integers define `mRn` if `m-n ` is a multiple of `12`. Prove the `R` is an equivalence relation.

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In the set Z of integers, define m Rn if m-n is a multiple of 12. Prove that R is an equivalence relation.

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Knowledge Check

  • Which of the following is not an equivalence relation on z?

    A
    aRb `hArr a+b` is an even integer
    B
    aRb <=> a-b is an even integer
    C
    `aRb hArr a lt b`
    D
    `aRb hArr a= b`

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