In the set Z of all integers, which of t

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

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)

Correct Answer:

x R y: if x ≤ y

Explanation:

If R is a relation defined by x R y: if x ≤ y, then R is reflexive and transitive. But, it is not symmetric.

Hence, R is not an equivalence relation.