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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.

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

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75.

Idempotent Laws

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

Let x be any arbitary element of $space space space space space space space open parentheses straight A union straight A close parentheses$

i.e. $space space space space space space space space space straight x element of open parentheses straight A union straight A close parentheses space rightwards double arrow space straight x element of straight A space space or space straight x element of straight A$

$space space space space space rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space straight x element of space straight A$

∴ $space space space space space space space space space space space space space space space straight x element of straight A left parenthesis straight A union straight A right parenthesis space space space space space space space space space rightwards double arrow space space space space space straight x element of straight A$

$space rightwards double arrow space space space space space space space space space open parentheses straight A union straight A close parentheses bottom enclose subset of space straight A$ ......(i)

Similarly we can show that $space space space space space space straight A space bottom enclose subset of space open parentheses straight A space union space straight A close parentheses$ ......(ii)

Using (i) and (ii), we get $space space space space space space space space space space space space space straight A space union space straight A$

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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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