### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Types of relation of a set, Equivalence Relation & Congruence Modulo Relation of Integers

Types of relation of a set

A relation on a set is called

(i) Reflexive:

(ii) Symmetric:

If

(iii) Transitive:

If and

and ; for

Equivalence Relation:

A relation is called an equivalence relation on if it is

(i) reflexive, (ii) symmetric, (iii) transitive

It is symbolically represents ‘‘.

Congruence Modulo Relation on Integers:

Let and be a fixed integer. We say that ‘ is congruent to modulo ‘ and written as divides .

Note:

In this case is of the form for some .

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