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Sets

Short Answer Type

141.

Assume that P ( A ) = P ( B ). Show that A = B

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142.
Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

No, Let A = {1, 2}, B = [2,3}

$rightwards double arrow$ $space space space space space space space space space space space space straight A space union space straight B space space space equals space left curly bracket 1 comma space 2 comma space 3 right curly bracket$

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$space space space space space space space space straight P left parenthesis bold B right parenthesis space equals space left curly bracket straight ϕ comma space left curly bracket 1 right curly bracket comma space left curly bracket 2 right curly bracket comma space left curly bracket 1 comma space 2 right curly bracket right curly bracket$

∴ $space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight P left parenthesis straight A right parenthesis space union space straight P left parenthesis straight B right parenthesis space equals space left curly bracket straight ϕ comma space left curly bracket 1 right curly bracket comma space left curly bracket 3 right curly bracket comma space left curly bracket 1 comma space 2 right curly bracket comma space left curly bracket 2 comma space 3 right curly bracket right curly bracket$ ...(i)

 $space space space space space space space space space space space space straight A union straight B space equals space left curly bracket 1 comma space 2 comma space 3 right curly bracket$

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

From (i) and (ii), it is clear that uin genera,

$space space space space space space space space space space space space space space space space space space space space space space space space straight P left parenthesis straight A right parenthesis union straight P left parenthesis straight B right parenthesis space not equal to space straight P left parenthesis straight A union straight B right parenthesis$

124 Views

143.

Out of 500 car owners investigated, 400 owned car A, 200 owned car B, and 50 owned both cars A and B. Is the data correct?

155 Views

144. A survey was conducted on 800 students of a school with regards to their interest in playing cricket and hockey. 576 of the students said they liked to play circket where as 360 liked to play hockey. What is the least number of students who liked to play both the games?

121 Views

145.

There are 200 individuals with skin disorder. 120 of them are exposed to chemical C_1,50 to chemical C₂ and 30 to both C₁ and C₂. Find the number of individuals :

(i) exposed to chemical C₁, but not to chemical C₂.

(ii) exposed to chemical C₂ but not to chemical C₁

(iii) exposed to C, or chemical C₂ or both.

(iv) not exposed to any of the chemicals C₁ and C₂.

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146. X and Y are two sets such that X has 28 elements, Y has 32 elements and X ∩ Y has 10 elements. How many elements does X ∪ Y have?

136 Views

147. If A and B are two sets and U is the universal set such that n(U) = 800, n( A) = 250, n(B) = 350 and n(A ∩ B) = 100. Find n(A' ∩ B')

129 Views

148. S and T are two sets such that S ∪ T has 60 elements. S has 35 elements and S ∩ T has 7 elements. How many elements set T have ?

124 Views

149. In a school, there are 20 teachers who teach Mathematics or Physics or both. 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics?

142 Views

150. In a committee, 50 people speak French, 20 speak Spanish and 10 speak both French and Spanish. How many of them speak at least one of the two languages ? If there are a total of 75 members in the committee, how many of them neither speak French nor Spanish ?

149 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

142. Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

142.
Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.