**CBSE Guide for Class 11 NCERT Mathematics | NCERT Answers for Class XI CBSE Matrhs**

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**Chapter 2 - relations and
functions**

**CBSE Guide, NCERT Solutions for Class 11 Mathematics Chapter 2 Exercise 2.2**

*(*__Cbse Ncert Solution of Class 11 Ncert Math Chapter 2, Relations and Functions__)
Question 1: Let A = {1, 2, 3…
14}. Define a relation R from A to A by

R = {(

*x*,*y*): 3*x*–*y*= 0, where*x*,*y*∈ A}. Write down its domain, codomain and range.__Solution__:

The relation R from A to A is given as -

R = {(

*x*,*y*): 3*x*–*y*= 0, where*x*,*y*∈ A}
Or, R = {(

*x*,*y*): 3*x*=*y*, where*x*,*y*∈ A}
∴
R = {(1, 3), (2, 6), (3, 9), (4, 12)}

The domain of R is the set of all first
elements of the ordered pairs in the relation.

∴
Domain of R = {1, 2, 3, 4}

The whole set A is the codomain of the
relation R.

∴
Codomain of R = A = {1, 2, 3… 14}

So, the range of R is the set of all second
elements of the ordered pairs in the relation.

∴ Range of R = {3, 6, 9, 12}

Question
2: Define a relation R on the set N

**of natural numbers by R = {(***x*,*y*):*y*=*x*+ 5,*x*is a natural number less than 4;*x*,*y*∈ N}. Depict this relationship using roster form. Write down the domain and the range.__Solution__:

R
= {(

*x*,*y*):*y*=*x*+ 5,*x*is a natural number less than 4,*x*,*y*∈ N}
The
natural numbers less than 4 are 1, 2, and 3.

∴ R = {(1, 6), (2, 7),
(3, 8)}

The
domain of R is the set of all first elements of the ordered pairs in the
relation.

∴ Domain of R = {1, 2,
3}

The
range of R is the set of all second elements of the ordered pairs in the
relation. ∴
Range of R = {6, 7, 8}

__Relations and Functions Exercise 2.2__

__|__*Class 11 Mathematics - Cbse Ncert Solution*|*CBSE Guide NCERT Answers*
Question 3: A = {1, 2, 3, 5} and B = {4, 6,
9}. Define a relation R from A to B by R = {(

*x*,*y*): the difference between*x*and*y*is odd;*x*∈ A,*y*∈ B}. Write R in roster form.__Solution__:

A = {1, 2, 3, 5} and B = {4, 6, 9}

R = {(

*x*,*y*): the difference between*x*and*y*is odd;*x*∈ A,*y*∈ B}
∴ R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}

Question 4: The given figure shows a
relationship between the sets P and Q. write this relation (i) in set-builder
form (ii) in roster form. What is its domain and range?

__Solution__:

According to the given figure, P = {5,
6, 7}, Q = {3, 4, 5}

(i) R = {(

*x, y*):*y = x*– 2;*x*∈ P} or R = {(*x, y*):*y = x*– 2 for*x*= 5, 6, 7}
(ii) R = {(5, 3), (6, 4), (7, 5)}

Domain of R = {5, 6, 7}

Range of R = {3, 4, 5}

__CBSE Guide NCERT Solutions of Class XI Ncert Math Chapter 2, Relations and Functions__

Question 5: Let A = {1, 2, 3, 4, 6}.

Let R be the
relation on A defined by {(a, b): a, b ∈ A, b is exactly divisible by a}.

(i) Write R in
roster form

(ii) Find the
domain of R

(iii) Find the
range of R.

__Solution__:

A = {1, 2, 3, 4, 6}, R = {(a, b): a, b ∈ A, b is
exactly divisible by a}

(i) R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6),
(3, 3), (3, 6), (4, 4), (6, 6)}

(ii) Domain of R = {1, 2, 3, 4, 6}

(iii) Range of R = {1, 2, 3, 4, 6}

Question 6: Determine the domain and range of
the relation R defined by

R = {(x, x +
5): x ∈ {0, 1, 2, 3, 4, 5}}.

__Solution__:

R = {(

*x*,*x*+ 5):*x*∈ {0, 1, 2, 3, 4, 5}}
∴
R = {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}

∴
Domain of R = {0, 1, 2, 3, 4, 5}

Range of R = {5, 6, 7, 8, 9, 10}

Question 7: Write the relation R = {(x, x3): x
is a prime number less than 10} in roster form.

__Solution__:

R = {(

*x*,*x*3):*x*is a prime number less than 10}
By the given condition the prime numbers less
than 10 are 2, 3, 5, and 7.

∴
R = {(2, 8), (3, 27), (5, 125), (7, 343)}

Question 8: Let A = {x, y, z} and B = {1, 2}.
Find the number of relations from A to B.

__Solution__:

It is given that A = {

*x*,*y*, z} and B = {1, 2}.
∴
A × B = {(

*x*, 1), (*x*, 2), (*y*, 1), (*y*, 2), (*z*, 1), (*z*, 2)}
Since

*n*(A × B) = 6, the number of subsets of A × B is 2^{6}.
Therefore, the number of relations from A to
B is 2

^{6}.
Question 9: Let R be the relation on Z defined
by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range
of R.

__Solution__:

R = {(a, b): a, b ∈ Z, a – b is an
integer}

It is known that the difference between any
two integers is always an integer.

∴
Domain of R = Z

Hence, Range of R = Z

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