Class 12 Maths Chapter 1 Relation and Function | Full Chapter | Engish Medium #ncert #boards #mpbse

Class 12 Maths Chapter 1 Relation and Function | Full Chapter | Engish Medium #ncert #boards #mpbse

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Reflexive Relations:
A relation R on a set A is reflexive if (a, a) ∈ R for every element a in A.

Symmetric Relations:
A relation R on a set A is symmetric if whenever (a, b) ∈ R, then (b, a) ∈ R as well.

Transitive Relations:
A relation R on a set A is transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.

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

Types of Functions:
One-to-one (Injective) Functions:
A function f: X → Y is one-to-one if f(x1) = f(x2) implies x1 = x2 for all x1, x2 in X.

Onto (Surjective) Functions:
A function f: X → Y is onto if for every y in Y, there exists an x in X such that f(x) = y.

Bijective Functions:
A function that is both one-to-one and onto is called bijective.

Composite Functions:
Given two functions f: X → Y and g: Y → Z, the composite function g o f is defined as (g o f)(x) = g(f(x)) for all x in X.

Invertible Functions:
A function f: X → Y is invertible if there exists a function g: Y → X such that g o f = IX (identity function on X) and f o g = IY (identity function on Y).

Binary Operations:
Binary operations are operations that combine two elements of a set to produce another element of the same set.

NCERT Exercises:
The NCERT textbook covers these topics through exercises, including

Empty relation
Universal relation
Reflexive relation
Symmetric relation
Transitive relation
Equivalence relation (a relation that is reflexive, symmetric, and transitive)
Defining and understanding binary operations
Properties like commutativity and associativity
Identity and inverse elements for binary operations

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