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NCERT Solution for Class 11 Maths Chapter 2: Relations and Functions Exercise 2.1





In this page we have NCERT Solution for Class 11 Maths Chapter 2: Relations and Functions Exercise 2.2 . Hope you like them and do not forget to like , social share and comment at the end of the page.
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.
Answer
The relation R from A to A is given as
R = {(x, y): 3x – y = 0, where x, y ∈ A}
i.e., R = {(x, y): 3x = y, where x, y ∈ A}
Therefore,
 R = {(1, 3), (2, 6), (3, 9), (4, 12)}
Domain of Relation
The set of all first elements of the ordered pairs in a relation R from a set
A to a set B is called the domain of the relation R.
Codomain of R
The whole set B is called the codomain of the
relation R
Range of Relation
The set of all second elements in a relation R from a set A to a set B is called the range of the relation R.
 
Therefore,
Domain of R = {1, 2, 3, 4}
The whole set A is the codomain of the relation R.
Therefore,
Codomain of R = A = {1, 2, 3... 14}
Therefore,
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.
Answer
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)}
 
Domain of Relation
The set of all first elements of the ordered pairs in a relation R from a set
A to a set B is called the domain of the relation R.
Codomain of R
The whole set B is called the codomain of the
relation R
Range of Relation
The set of all second elements in a relation R from a set A to a set B is called the range of the relation R.
 
Therefore, Domain of R = {1, 2, 3}
Therefore, Range of R = {6, 7, 8}
 
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.
Answer
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}
Therefore, 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?
ncert-solution-class11-maths-relation-and-function-1.png
Answer
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}
 
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.
Answer 5
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}}.
Answer 6
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.
Answer
R = {(x, x3): x is a prime number less than 10}
The prime numbers less than 10 are 2, 3, 5, and 7.
Therefore, 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.
Answer 8
Given that A = {x, y, z} and B = {1, 2}.
Cartesian Product: 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.
Answer 9
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.
Therefore, Both the domain and range would be Z
Domain of R = Z
Range of R = Z


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