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81.
Let A = { a, b }, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?

(a) a = {a, b}, B = {a, b, c}

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight a space element of space straight A comma space space space space space space space space space space rightwards double arrow space space space space space space straight a space element of space space straight B space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight b space element of space straight A comma space space space space space space space space space space space rightwards double arrow space space space space space straight b space element of space straight B$

∴ Every number of set A is also a member of set B.

∴ $space space space space space space space space space space space space space space space space space space space space space straight A space bottom enclose subset of space straight B space space space space space space space space space space space space space space space space space space space space space Also comma space straight c element of straight B space and space straight c not an element of space straight A space space space space space space space space space space space space space space space space space space space space space Hence comma space straight A space subset of space straight B$

Also, $space space space space space space space space space space space space space space space space space straight A space union space straight B space equals space left curly bracket straight a comma space straight b right curly bracket space union space left parenthesis straight a comma space straight b comma space straight c right parenthesis space equals space left curly bracket straight a comma space straight b comma space straight c right curly bracket space equals space straight B$

106 Views

82.

If A and B are two sets such that A ⊂ B, then what is A ∪ B?

105 Views

83.

Which of the following pairs of sets are disjoint?

(i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 }

(ii) { a, e, i, o, u } and { c, d, e, f }

(iii) {x : x is an even integer } and {x : x is an odd integer}

123 Views

84.

Write all the proper subsets of the set A = {1, 3, 5}.

97 Views

85.

Let A = {2, 3, 6, 8}, Find (a) P(A) and (b) n[P(A)].

136 Views

86.

Write $space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight a right parenthesis space space space space straight P left parenthesis straight ϕ right parenthesis space and space straight n left square bracket straight P left parenthesis straight ϕ right parenthesis right square bracket space space space space left parenthesis straight b right parenthesis space space space straight P left curly bracket straight ϕ right curly bracket space and space straight n left curly bracket straight P left curly bracket straight ϕ right curly bracket right square bracket space space space space space space left parenthesis straight c right parenthesis space space straight P left curly bracket straight ϕ comma space left curly bracket straight ϕ right curly bracket right curly bracket space space space and space straight n left curly bracket straight P left curly bracket straight ϕ comma space left curly bracket straight ϕ right curly bracket right curly bracket right square bracket$

102 Views

87.

Which of the following sets are comparable?

A = {a, b, c}, B = {b, c, d}, C = {b, c, d, e}, D = {a, b, c, ,e}

116 Views

88.

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

103 Views

89.

A = { a, i, o}, B = { e , o, i}, C = {i, ,e, o, u}, D = $space space space space space space space space space left curly bracket straight ϕ right curly bracket$ Write a suitable universal set for A, B, C, and D.

103 Views

90.

Mark the following subsets of set R or real numbers, on the number line :

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight a right parenthesis space space left curly bracket straight x space colon space straight x space element of space straight R comma space minus 4 space less or equal than space straight x space less or equal than space 2 right curly bracket space space space space space left parenthesis straight b right parenthesis space left curly bracket straight x space colon space straight x space element of space straight R comma space minus 4 space less than space straight x space less or equal than space 0 right curly bracket space space space space left parenthesis straight c right parenthesis space left curly bracket straight x space colon space straight x colon space element of space straight R comma space 2 space less or equal than space straight x space less than space 6 right curly bracket space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight d right parenthesis space space left curly bracket straight x space colon space straight x space element of space straight R comma space 4 space less than space straight x space less than space 7 right curly bracket$