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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.

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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?

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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?

Set A = set ofstudents who liked to play cricket

$rightwards double arrow$ n(A) = 576 ...(i)

Set B = set of students who liked to play hockey

$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ n(B) = 360 ....(ii)

U = set of students surveyed

$space rightwards double arrow space space space space space space space space space space space space space space space space straight n left parenthesis straight U right parenthesis space equals space 800$

Now, $space space space space space space space space space space space space space space straight n open parentheses straight A union straight B close parentheses space less or equal than space straight n space left parenthesis straight U right parenthesis$ ....(ii)

Using, $space space space space space space space space space space space space space space space space space space straight n left parenthesis straight A union straight B right parenthesis space equals space straight n left parenthesis straight A right parenthesis plus straight n left parenthesis straight B right parenthesis minus straight n left parenthesis straight A intersection straight B right parenthesis$ , we get

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight n left parenthesis Aub right parenthesis space equals space 576 space plus space 360 space minus space straight n left parenthesis straight A intersection straight B right parenthesis$

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

Putting in (iii), we have

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

$rightwards double arrow space space space space space$ $space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus straight n left parenthesis straight A intersection straight B right parenthesis space equals space 936 minus straight n left parenthesis straight A intersection straight B right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space straight n left parenthesis straight A intersection straight B right parenthesis space greater or equal than space 136$

Hence, the least number of students who like to play both games = 136.

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?

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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')

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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 ?

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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?

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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 ?

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