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Solutions ⇒ Class 11th ⇒ Mathematics ⇒ 2. Relations and Functions

Exercise 2.2 Class 11 maths 2. Relations and Functions - ncert solutions - Toppers Study

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Exercise 2.2 Class 11 maths 2. Relations and Functions - ncert solutions - Toppers Study

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Exercise 2.2 class 11 Mathematics Chapter 2. Relations and Functions

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2. Relations and Functions

| Exercise 2.2 |

Exercise 2.2 Class 11 maths 2. Relations and Functions - ncert solutions - Toppers Study


Exercise 2.2


Q1. 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} 

Given, R = {(x, y): 3x - y = 0, where x, y ∈ A} 

3x - y = 0 

∴ 3x = y 

Putting value x= 1, 2, 3, 4 from A we have y = 3, 6, 9, 12 

∴ 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 R.

∴ Domain of R = {1, 2, 3, 4}

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

∴ Co-domain of R = {1, 2, 3… 14}

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

∴Range of R = {3, 6, 9, 12} 

Q2. 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 R.

∴ Domain of R = {1, 2, 3}

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

∴ Range of R = {6, 7, 8} 

Q3. 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)} 

Q4. The Fig 2.7 shows a relationship between the sets P and Q. Write this relation

(i) in set-builder form

(ii) roster form.

What is its domain and range?

Solution: From the given figure, we have

A = {5, 6, 7}, B = {3, 4, 5}

(i)R = {(x, y): y = x – 2; x ∈ A and y ∈ B} 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}

Q5. 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} 

Q6. 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} 

Q7. 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, x3): x is a prime number less than 10}

The prime numbers less than 10 are 2, 3, 5, and 7.

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

Q8. Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B. 

Solution: 

 Given: 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.

the number of relations from A to B is 26

Q9. 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

   Range of R = Z 

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Mathematics Class - 11th

NCERT Maths book for CBSE Students.

books

Study Materials List:

Solutions ⇒ Class 11th ⇒ Mathematics
1. Sets
2. Relations and Functions
3. Trigonometric Functions
4. Principle Of Mathematical Induction
5. Complex Numbers and Quadratic Equations
6. Linear Inequalities
7. Permutations and Combinations
8. Binomial Theorem
9. Sequences and Series
10. Straight Lines
11. Conic Sections
12. Introduction to Three Dimensional Geometry
13. Limits and Derivatives
14. Mathematical Reasoning
15. Statistics
16. Probability

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