# Class 11 Maths NCERT Solutions For Chapter 2 Relations and Functions

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## In this pdf file you can see answers of following Questions

### EXERCISE  2.1

Qusetion 1. If 1 2 5 1 3 3 33 , find the values of x and y.

Question 2. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).

Question 3. If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

Question 4. State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.
(i) If P = {m, n} and Q = { n, m}, then P × Q = {(m, n),(n, m)}.
(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B.
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ φ) = φ.

Question 5. If A = {–1, 1}, find A × A × A. 6. If A × B = {(a, x),(a , y), (b, x), (b, y)}. Find A and B.

Question 6. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that (i) A × (B ∩ C) = (A × B) ∩ (A × C). (ii) A × C is a subset of B × D.

Question 7. Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

Question 8. Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.

10. The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A and the remaining elements of A × A

### EXERCISE Question 2.2

Qusetion 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.

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.

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.

Question 4. The Fi 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?

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.

Question 6. Determine the domain and range of the relation R defined by R = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4, 5}}.

Question 7. Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form.

Question 8. Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

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.

### EXERCISE 2.3

Qusetion 1. Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
(i) {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}
(ii) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}
(iii) {(1,3), (1,5), (2,5)}.

Question 2. Find the domain and range of the following real functions: (i) f(x) = – x (ii) f(x) = 9 − x 2.

Question 3. A function f is defined by f(x) = 2x –5. Write down the values of (i) f (0), (ii) f (7), (iii) f (–3).

Question 4. The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by t(C) = 9C 5 + 3 2.Find
(i) t(0)
(ii) t(28)
(iii) t(–10)
(iv) The value of C, when t(C) = 212.

Question 5. Find the range of each of the following functions.
(i) f (x) = 2 – 3x, x ∈ R, x > 0.
(ii) f (x) = x2 + 2, x is a real number.
(iii) f (x) = x, x is a real number

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