11th NCERT Relatins and functions. Exercise 2.2 Questions 9
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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

Let A = {1, 2, 3, … , 14}.
R : A → A
R = {(x, y): 3x – y = 0, where x, y ∈ A}.
R = { (1,3),(2,6),(3,9),(4,12)}
Domain of R = { 1, 2, 3, 4}
Codomain of R = { 1, 2, 3, ....14} = A.
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 : N → N,
R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}.
x = 1, 2, 3,
R = {(1,6),(2,7),(3,8)}
The domain of R = {1, 2, 3}
The 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.

Solution

A = {1, 2, 3, 5} and B = {4, 6, 9}.
R : A → B
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.
(iii) What is its domain and range?

Solution

R : P → Q
(i) In set builder form.
R = { (x,y) : y = x - 2 , x ∈ P, y ∈ Q}
(ii) Roster form
R = {(5,3), (6,4), (7,5)}
(iii) 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.

Solution

A = {1, 2, 3, 4, 6}.
R : A → A
R = {(a, b): a, b ∈ A, b is exactly divisible by a}.
(i) Roster form
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 og 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)}
So 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}
So the relation R in roaster form is
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

Let A = {x, y, z} and B = {1, 2}.
n(a) = m = 3, n(B) = n = 2.
The number of relations = (2m)n
= (23)2
= 2 6
= 64.

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 : Z → Z
R = {(a, b): a, b ∈ Z, a – b is an integer}. R = {......., ( -1,0),(-1,1), (-1,2),....,(0,-1),(0,0).....}
So domain of R = {....-2, -1, 0, 1, 2,....} = Z
And range of R = { ....-2, -1, 0, 1, 2,....} = Z
Exercise 2.1 ⇐
⇒ Exercise 2.3