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Sets

Short Answer Type

81.

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

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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}

(i) A = {1, 2, 3, 4},

$space space space space space space space space space space space space space space space space space space space space space space space space space space space straight B space equals space space space space space space space space space left curly bracket space straight x thin space space colon space straight x space element of space straight N comma space space 4 space less or equal than space straight x space less or equal than space right curly bracket space equals space left curly bracket 4 comma space 5 comma space 6 right curly bracket space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space straight A space intersection space straight B space equals space left curly bracket 1 comma space 2 comma space 3 comma space 4 right curly bracket space intersection space left curly bracket 4 comma space 5 comma space 6 right curly bracket space equals space left curly bracket 4 right curly bracket space equals straight ϕ$

Hence, A and B are not disjoint sets.

(ii) A = { a, e, i, o, u }, B = { c, d, e, f }

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

∴ A and B are not disjoint sets.

(iii) A = {x : x is an even integer}
= {........, -6, -4, -2, 0, 2, 4, 6, 8, 10, ................}

B = {and {x : x is an odd integer} = {........., -5, -3, -1, 1, 3, 5, 7, .............}

$space space space space space space space space space space rightwards double arrow space space space space space straight A space intersection space straight B space equals space left curly bracket space space space right curly bracket space equals space straight ϕ$

Hence, A and B are disjoint sets.

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 :

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

106 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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}

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}