Question

1. The figure shows a relation between the sets P and Q Based on the above information answer the following: (i) This relation in set builder form is (a) R={(x,y): x is square root of y} (b) R={(x,y) : y is square of x} (c)R={(x,y): x is square of y} (d) None of above (ii) The domain of relation is (a) {1,2,3,4,5} (b) {4,9,25,5} (c) {4,9} (d) {4,9,25} (iii) The range of relation is (a) {4,9,25} (b) {1,2,3,4,5} (c) {-2,2,-3,3,-5,5} (d) {-5,-3,-2,1,2,3,5} (iv) The relation in roster form is (a) {(9,3), (4,2),(25,5) } (b) {(9,3),(9,-3),(4,2),(4,-2),(25,5),(25,-5)} (c){(9,-3),(4,-2),(25,-5)} (d) None of above (v) The total number of relation from P to Q is (a) 32 (b) 64 (c) 128 (d) None of above​

Answer 1

SOLUTION

TO EVALUATE

To answer the given questions

EVALUATION

ANSWER TO QUESTION : (i)

Under the relation R every element of P is related to two elements of Q

4 is related to - 2 and 2

9 is related to - 3 and 3

25 is related to - 5 and 5

Thus we see that if (x, y) ∈ R then x is a square of y

So the relation in set builder form is (a) R = {(x,y) : x is square root of y }

Hence the correct option is

(a) R = { (x,y) : x is square root of y }

ANSWER TO QUESTION : (ii)

We see that the elements of P are 4 , 9 , 25

Also the domain of relation is (d) { 4 , 9 , 25 }

Hence the correct option is

(d) { 4 , 9 , 25 }

ANSWER TO QUESTION : (iii)

We observe that if (x, y) ∈ R then x is a square of y

4 is related to - 2 and 2

9 is related to - 3 and 3

25 is related to - 5 and 5

So the required range is {-2,2,-3,3,-5,5}

Hence the correct option is

(c) {-2,2,-3,3,-5,5}

ANSWER TO QUESTION : (iv)

From given figure we observe that if (x, y) ∈ R then x is a square of y

4 is related to - 2 and 2

9 is related to - 3 and 3

25 is related to - 5 and 5

So the elements of R are (9,3),(9,-3),(4,2),(4,-2),(25,5),(25,-5)}

Hence the correct option is

(b) {(9,3),(9,-3),(4,2),(4,-2),(25,5),(25,-5)}

ANSWER TO QUESTION : (v)

Number of elements in P = 3

Number of elements in Q = 7

So the total number of relations

$\sf{ = {2}^{(3 \times 7)} }$

$\sf{ = {2}^{21} }$

Hence the correct option is

(d) None of above

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