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In the Set Z of All Integers, Which of the Following Relation R is Not an Equivalence Relation ? - Mathematics

MCQ

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)

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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.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 1 Relations
Exercise 1.4 | Q 26 | Page 33
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