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.

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written 9.0 years ago by

teamques10 ★ 70k

modified 3.8 years ago by

pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: Dec 2013

discrete mathematics

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written 9.0 years ago by

teamques10 ★ 70k

• modified 9.0 years ago

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

R is reflexive:

Since a-a=0=0.m, Ɏ a € I, aRa.

Hence, R is reflexive.
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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