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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)

109 Views

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

99 Views

13.
If A × B = {(a, x),(a , y), (b, x), (b, y)}. Find A and B.

A x B = {(p, q), (p, r), (m, q), (m, r)}

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight p comma straight q right parenthesis element of straight A cross times straight B space rightwards double arrow space straight p element of straight A comma straight q element of straight B$

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$space space space space space space space space space space space space space space space space space space space left parenthesis straight m comma space straight q right parenthesis element of straight A space cross times space straight B space rightwards double arrow space straight m element of straight A comma space straight q element of straight B$

$space space space space space space space space space space space space space left parenthesis straight m comma space straight r right parenthesis element of straight A space cross times space straight B space rightwards double arrow space straight m element of straight A comma space straight r element of straight B$

Hence, A = {p, m), B = {q, r}

189 Views

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.

166 Views

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

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100 Views

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

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