Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Chapter-2. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-2 (a), Exe-2 (b), Exe-2 (c), Exe-2 (e), Exe-2 (f) and Exe-2 (g) Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.
Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions
Class: | 11th |
Subject: | Mathematics |
Chapter : | Ch-2 Relation and Mapping of Section -A |
Board | ISC |
Writer | OP Malhotra |
Publications | S.Chand Publications 2020-21 |
-: Select Topics :-
Relations and Functions Class 11 Chapter 2
Before we start learning about relations and functions class 11, let us go through some basics of sets. As we learned, a set is a collection of objects or elements. You have also learned about the empty set, universal set and all the other types in sets for class 11
Cartesian Product of Sets
Suppose there are two non-empty sets A and B. So, the cartesian product of A and B is the set of all ordered pairs of elements from A and B.
A × B = {(a,b) : a ∊ A, b ∊ B}
Let A = {a1, a2, a3, a4} and B = {b1, b2}
Then, The cartesian product of A and B will be;
A × B = {(a1, b1), (a2, b1), (a3, b1), (a4, b1), (a1, b2), (a2, b2), (a3, b2), (a4, b2)}
Example: Let us say, X = {a,b,c} and Y = { 1,2,3}
Definition of Relations:
A relation R is the subset of the cartesian product of X x Y, where X and Y are two non-empty elements. It is derived by stating the relationship between the first element and second element of the ordered pair of X × Y. The set of all primary elements of the ordered pairs is called a domain of R and the set of all second elements of the ordered pairs is called a range of R.
Functions
A relation ‘f’ is said to be a function, if every element of a non-empty set X, has only one image or range to a non-empty set Y.
Or
If ‘f’ is the function from X to Y and (x,y) ∊ f, then f(x) = y, where y is the image of x, under function f and x is the preimage of y, under ‘f’. It is denoted as;
f: X → Y.
Functions
A relation ‘f’ is said to be a function, if every element of a non-empty set X, has only one image or range to a non-empty set Y.
Or
If ‘f’ is the function from X to Y and (x,y) ∊ f, then f(x) = y, where y is the image of x, under function f and x is the preimage of y, under ‘f’. It is denoted as;
f: X → Y.
Inverse of Relation
For any two non-empty sets A and B. Let R be a relation from a set A to a set B. Then, the inverse of relation R, denoted by R-1 is a relation from B to A and it is defined by
R-1 ={(b, a) : (a, b) ∈ R}
Domain of R = Range of R-1 and
Range of R = Domain of R-1.
Functions
A relation f from a set A to set B is said to be function, if every element of set A has one and only image in set B.
In other words, a function f is a relation such that no two pairs in the relation have the first element.
Real-Valued Function
A function f : A → B is called a real-valued function if B is a subset of R (set of all real numbers). If A and B both are subsets of R, then f is called a real function.
Some Specific Types of Functions
Identity function: The function f : R → R defined by f(x) = x for each x ∈ R is called identity function.
Domain of f = R; Range of f = R
Constant function: The function f : R → R defined by f(x) = C, x ∈ R, where C is a constant ∈ R, is called a constant function.
Domain of f = R; Range of f = C
Polynomial function: A real valued function f : R → R defined by f(x) = a0 + a1x + a2x2+…+ anxn, where n ∈ N and a0, a1, a2,…….. an ∈ R for each x ∈ R, is called polynomial function.
Rational function: These are the real function of type 𝑓(𝑥)𝑔(𝑥), where f(x)and g(x)are polynomial functions of x defined in a domain, where g(x) ≠ 0.
The modulus function: The real function f : R → R defined by f(x) = |x|
or
for all values of x ∈ R is called the modulus function.
Domaim of f = R
Range of f = R+ U {0} i.e. [0, ∞)
Signum function: The real function f : R → R defined
by f(x) = |𝑥|𝑥, x ≠ 0 and 0, if x = 0
or
Exe-2(a),
Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions
Page No-(2-6)
Exe-2 (b),
Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions
Page No-(2-11)
Exe-2 (c),
Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions
Page No-(2-19)
Exe-2 (d),
Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions
Page No-(2-28)
Exe-2 (e),
Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions
Page No-(2-36)
Exe-2 (f)
Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions
Page No-(2-43)
Exe-2 (g)
Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions
Page No-(2-57)
-: End of Relation and Mapping Solution :-
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