Asked by inderjeet.saluja | 27th Aug, 2014, 12:27: AM
The Relation R is an equivalence relation if and only if it satisfies the properties, Reflexivity, Symmetry and Transitivity.
Reflexivity: a is related to a because a-a is zero and zero divisible by any number and hence R is reflexive.
Symmetry: Assume that a is related to b, and hence a-b is divisible by m
Since a and b are integers, we have, and hence both are divisible by m.
Thus, R is Symmetric.
Transitivity: Iif a is related to b, we have,
If b is related to c, we have,
Thus, a - c is divisible by m and hence a is related to c.
Thus, R is transitive.
Hence R is an equivalence relation.
Answered by Vimala Ramamurthy | 27th Aug, 2014, 08:59: AM
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