First slide

Introduction to Relations (XI) on Sets

Question

Which of the following is not an equivalence relation on I

Easy

A

$a R b$ if $(a + b)$ is an even integer
B

$a R b$ if $(a - b)$ is an even integer
C

$a R b$ if $a < b$
D

$a R b$ if $a = b$

Solution

The relations given in options 1, 2, 4 are clearly equivalence. But option 3 is transitive but not reflexive & symmetric.

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