# Plus One Math's Solution Ex 2.2 Chapter2 Relations and Functions

In this chapter, you are provided with several diagrams and examples along with their solutions for a clear understanding of Relations and Functions. To know more about
Class 11 Maths Chapter 2 Relations and Functions, you should explore the exercises below. You can also download the Sets Class 11 NCERT Solutions PDF

In this chapter, you’ll get a clear understanding of Relations and Functions. Both Relations and Functions have a different meaning in mathematics; however many get confused and use these words interchangeably. A ‘relation’ means a relationship between two elements of a set.  It is a set of inputs and outputs, denoted as ordered pairs (input, output). We can also represent a relation as a mapping diagram or a graph. A relation can either be symbolised by Roster method or Set-builder method. On the other hand, a ‘function’ is a special type of relation, in which each input is related to a unique output. So, all functions are relations, but not all relations are functions.

 Board SCERT, Kerala Text Book NCERT Based Class Plus One Subject Math's Textbook Solution Chapter Chapter 2 Exercise Ex 2.2 Chapter Name Relations and Functions Category Plus One Kerala

## Kerala Syllabus Plus One Math's Textbook Solution Chapter  2 Relations and Functions Exercises 2.2

### Chapter  2  Relations and Functions Textbook Solution

• Exercises 2.1
• Exercises 2.2
• Exercises 2.3
• Miscellaneous Exercise Chapter 2

• Kerala plus One maths NCERT textbooks, we provide complete solutions for the exercise and answers provided at the end of each chapter. We also cover the entire syllabus given by the Board of secondary education, Kerala state.

### Chapter  2  Relations and Functions Exercise   2.2

Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(xy): 3x – y = 0, where xy ∈ A}. Write down its domain, codomain and range.

The relation R from A to A is given as

R = {(xy): 3x – y = 0, where xy ∈ A}

i.e., R = {(xy): 3x = y, where xy ∈ 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 codomainof the relation R.

∴Codomain of R = A = {1, 2, 3, …, 14}

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}

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

R = {(xy): y = x + 5, x is a natural number less than 4, xy ∈ 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}

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(xy): the difference between x and y is odd; x ∈ A, ∈ B}. Write R in roster form.

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

R = {(xy): the difference between x and y is odd; x ∈ A, ∈ B}

∴R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}

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?

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}

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by

{(ab): ab ∈ 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.

A = {1, 2, 3, 4, 6}, R = {(ab): ab ∈ 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}

Determine the domain and range of the relation R defined by R = {(xx + 5): x ∈ {0, 1, 2, 3, 4, 5}}.

R = {(xx + 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}

Write the relation R = {(xx3): is a prime number less than 10} in roster form.

R = {(xx3): 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)}

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

It is given that A = {xy, 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.

Let R be the relation on Z defined by R = {(ab): ab ∈ Z– b is an integer}. Find the domain and range of R.

R = {(ab): ab ∈ Z– 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

#### Chapter 2: Relations and Functions EX 2.2 Solution- Preview

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