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Let m be the positive integers greater than 1. Show that the relation $R =\{(a,b)|a \equiv b (mod \ \ m)\}$, i.e. aRb if and only if m divides a-b, is an equivalent relation on the set of integers.
written 7.4 years ago by gravatar for teamques10 teamques10 ★ 65k modified 2.3 years ago by gravatar for pedsangini276 pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: Dec 2013
discrete mathematics
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written 7.4 years ago by gravatar for teamques10 teamques10 ★ 65k •   modified 7.4 years ago

Let a, b € I where I be the set of Integers.

  1. R is reflexive:

    Since a-a=0=0.m, Ɏ a € I, aRa.

    Hence, R is reflexive.

  2. R is symmetric:

    Suppose aRb

    a-b is divisible by m.

    a-b = k.m for some integer k,

    b-a = (-k).m for some integer –k. …

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