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Question
In the set Z of all integers, which of the following relation R is not an equivalence relation ?
Options
x R y : if x ≤ y
x R y : if x = y
x R y : if x − y is an even integer
x R y : if x ≡ y (mod 3)
Solution
x R y : if x ≤ y
Clearly, R is not symmetric because x < y does not imply y < x.
Hence, (a) is not an equivalence relation.
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