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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.

n(A x A) = 9

$rightwards double arrow$ n(A) c n(A) = 9 $rightwards double arrow$ n(A) = 3

$space space space space space space space space space space space space space space space space space space space space left parenthesis negative 1 comma 0 right parenthesis element of straight A space straight x space straight A rightwards double arrow negative 1 element of straight A comma space 0 element of straight A$

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$rightwards double arrow$ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

Also, n(A) = 3 $rightwards double arrow$ A = (-1, 0, 1)

Hence, A = {-1, 0, 1}

Also, A x A = {-1, 0, 1} x {-1, 0, 1}

= {(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1)}

Hence, the remaining elements of A x A are

(-1, -1), (-1, 1), (0, -1), (0, 0), (1, -1), (1, 0) and (1, 1).

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 :

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