Notes Sets, Relation & Inequalities

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Course:	MATHS FOR JEE
Book:	Notes Sets, Relation & Inequalities

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Date:	Saturday, 18 May 2024, 9:22 PM

1. Inequalities

Equivalence relation:
A relation which is reflexive, symmetric and transitive is called an equivalence relation.

Illustrative examples:
Ex. 1: Let

be a relation on

, defined by

Show that

is an equivalence relation.
Solution: Given

and

i) Let

then

So,

is reflexive.

ii)

i.e.

is an integer

Thus

is symmetric.
iii) (a, b)

and

is an integer and

is an integer

Thus

and

is transitive.

Thus,

is reflexive, symmetric and transitive.

is an equivalence relation.