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Relations and Functions

Short Answer Type

11. Let A = {–1, 1}, B = {2, 3}, C = {3, 5} be subsets of real numbers.

n(A X A X A)

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12. Let A = {1,2, 3, 4}

space space space space space space space space space space space straight S space equals space left curly bracket left parenthesis straight a comma space straight b right parenthesis space colon space straight a element of straight A comma space straight b space element of space straight A comma space straight a space divides space straight b right curly bracket

space space space space space space space space straight B space equals space left curly bracket straight x space colon space straight x element of straight A comma space straight x space is space straight a space prime right curly bracket

Write (i) S explicity, (ii) B explicity, (iii) S x B

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13.

If A × B = {(a, x),(a , y), (b, x), (b, y)}. Find A and B.

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14.

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.

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15. Let A = {I, 2, 3}, B = {2, 3, 4} and C = {4, 5}. Verify that :

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16. Let A = {I, 2, 3}, B = {2, 3, 4} and C = {4, 5}. Verify that :

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight A cross times open parentheses straight B union straight C close parentheses equals left parenthesis straight A cross times straight B right parenthesis union left parenthesis straight A cross times straight C right parenthesis$

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17. Find the values of x and y when

(2x, x+y) = (6, 2)

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18.

If A = {a, b, c} and B = {p, q}, then find :

A x B

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19. Let A = {I, 2, 3}, B = {2, 3, 4} and C = {4, 5}. Verify that :

A x (B - C) = (A x B) - (A x C)

B - C = {2, 3, 4} - {4, 5} = {2, 3}

∴ A x (B - C) = {1, 2, 3} x {2, 3} = {(1, 2), (1, 3), (2, 2), (2, 3), (3,. 2), (3, 3)} ....(i)

(A x B)-(A x C) = {1, 2, } x {1, 3}, {1, 4}, {2, 2}, {2, 3}, {2, 4}, {3, 2}, {3, 3},{3, 4} - {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)

= {(1, 2), (1, 3), (2, 2), (2, 3), (3, 2), (3, 3)} .....(ii)

Hence, from (i) and (ii), we have

A x (B - C) = (A x B) - (A x C)

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