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Class XI Mathematics NCERT Solutions

RELATIONS AND FUNCTIONS

Exercise 2.2

Answers

1. Given: A = {1, 2, 3, .., 14}

The ordered pairs which satisfy 3 0x y = are (1, 3), (2, 6), (3, 9) and (4, 12). R = {(1, 3), (2, 6), (3, 9), (4, 12)}

Domain = {1, 2, 3, 4}

Range = {3, 6, 9, 12}

Co-domain = {1, 2, 3, .., 14}

2. Given: R = ( ){ }, : 5, is a natural number less than 4 : , Nx y y x x x y= + Putting x = 1, 2, 3 in 5,y x= + we get y = 6, 7, 8 R = {(1, 6), (2, 7), (3, 8)}

Domain = {1, 2, 3}

Range = {6, 7, 8}

3. Given: A = {1, 2, 3, 5} and B = {4, 6, 9}, x A, y B x y = (1 4), (1 6), (1 9), (2 4), (2 6), (2 9), (3 4), (3 6) (3 9), (5 4), (5 6), (5 9)

3, 5, 8, 2, 4, 7, 1, 3, 6,1, 1, 4x y = R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6) (5, 4), (5, 6)}

4. (i) Relation R in set-builder form is R = ( ){ }, : 2 : 5,6,7x y y x x= = (ii) Relation R in roster form is R = {(5 3), (6, 4), (7, 5)

Domain = {5, 6, 7}

Range = {3, 4, 5}

5. Given: A = {1, 2, 3, 4, 6}

A set of ordered pairs ( ),a b where 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), (4, 6)}

(ii) Domain of R = {1, 2, 3, 4, 6}

(iii) Range of R = {1, 2, 3, 4, 6}

6. Given: R = ( ) ( ){ }, 5 : 0,1, 2,3, 4,5x x x+ = ( ){ }, : 0,1,2,3,4,5a b a = a x= and 5b x= + Putting 0,1, 2,3, 4,5a = we get 5,6,7,8,9,10b = Domain of R = {0, 1, 2, 3, 4 5}

Range of R = {0, 1, 2, 3, 4 5}

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7. Given: R = ( ){ }3, : is a prime number less than 10x x x Putting x = 2, 3, 5, 7

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

8. Given: A = { }, ,x y z and B = {1, 2} Number of elements in set A = 3 and Number of elements in set B = 2

Number of subsets of A x B = 3 x 2 = 6

Number of relations from A to B = 26.

9. Given: R = ( ){ }, : , Z, is an integera b a b a b = ( ){ }, : , Z, both and are even or both and are odda b a b a b a b = ( ) ( ) ( ){ }, : , Z, and are even and are odda b a b a b a b

Domain of R = Z

Range of R = Z