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Sets

Short Answer Type

71. Let A, B, C, be three sets. If A ∪ Band B ∊ C, then A ∊ C. Is the statement true ? If not give example.

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72.

Distributive Laws

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73.

Write the following intervals in the set-builder form and mark them on the number line.

(i) (-3,0) (ii) [6, 12] (iii) (6, 12]

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74.
$space space space space space space space space space space space space space space space space space space open parentheses straight A union straight B close parentheses union straight C$

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

$space space space space space space space space space space space space space space straight x space element of space open parentheses straight A union straight B close parentheses union straight C space rightwards double arrow space straight x element of open parentheses straight A union straight B close parentheses space or space straight x element of subset of$

$rightwards double arrow$    $space space space space space space space space space space space space space space space space space space open parentheses straight x element of straight A space space or space straight x space element of space straight B close parentheses space or space straight x space element of subset of$

$rightwards double arrow$    $space space space space space space space space space space straight x element of straight A space or space left parenthesis straight x element of straight B space or space straight x element of subset of right parenthesis$

$rightwards double arrow$    $space space space space space space space space space space space space space straight x space element of space straight A space or space straight x space element of space left parenthesis straight B union straight C right parenthesis space space space space space space rightwards double arrow space space space space straight x space straight e space straight A space union space left parenthesis straight B space union space straight C right parenthesis$

Thus, $space space space space space space space space space space straight x space element of space left parenthesis straight A space union space straight B right parenthesis space union space straight C space rightwards double arrow space straight x element of space straight A space union space straight B left parenthesis straight B union straight C right parenthesis$

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75.

Idempotent Laws

$space space space space space space space space space straight A space union space straight A space equals space straight A$

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76. Identity Laws

$space space space space space space space space space space space space space space space space left parenthesis straight i right parenthesis space straight A space union space straight X space equals space straight X space space space space space space space space space space space space left parenthesis Ii right parenthesis space space straight A space union space straight ϕ space equals space straight A space space space space space space left parenthesis iii right parenthesis space straight A space intersection space straight phi space equals space straight ϕ$

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77.

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78.

If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }; find (i) A – B (ii) A – C (iii) A – D (iv) B – A (v) C – A (vi) D – A (vii) B – C (viii) B – D (ix) C – B (x) D – B (xi) C – D (xii) D – C.

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79.

If a =- {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8}, D = {7, 8, 9, 10}, Find

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

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80.

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15}and D = {15, 17}; find (i) A ∩ B (ii) B ∩ C (iii) A ∩ C ∩ D (iv) A ∩ C (v) B ∩ D (vi) A ∩ (B ∪ C) (vii) A ∩ D (viii) A ∩ (B ∪ D) (ix) ( A ∩ B ) ∩ ( B ∪ C ) (x) ( A ∪ D) ∩ ( B ∪ C)

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