# Relations and Functions - NCERT Solutions for CBSE Class 11 Mathematics Chapter 2 Exercise 2.2 | CBSE Math Guide

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

### 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): 3x 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): 3x y = 0, where x, y ∈ A}
Or, R = {(x, y): 3x = 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, x3): 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 26.
Therefore, the number of relations from A to B is 26.
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