Relations and Functions

Relations and Functions

Question

In a group of 950 residents of a locality, every resident is fond of reading at least one of the morning newspapers published in English and Hindi. 750 of them like to read Hindi newspaper and 460 read the English newspapers. Find how many of them read

(i) Both the English newspaper and the Hindi newspaper.

(ii) English newspaper only.

(iii) Hindi newspaper only.

Answer

Set A = set of residents who read Hindi newspapers
rightwards double arrow                n(A) = 750                                                                                             ....(i)
B = Set of resident who like to read English newspapers
rightwards double arrow               n(B) = 460                                                                                               ....(ii)
Also,     space space space space space space space space space space space straight n left parenthesis straight A union straight B right parenthesis = 950                                                                                         ....(iii)
Using,    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 space plus straight n left parenthesis straight B right parenthesis space 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 950 space equals space 750 plus space 460 space minus space straight n left parenthesis straight A intersection straight B right parenthesis
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 straight n left parenthesis straight A intersection straight B right parenthesis space space equals space 750 plus 460 minus 950 equals 260
Hence, the number of residents who like to read
(i) Both the newspapers        = space space space space space space space space space space space space space straight n left parenthesis straight A intersection straight B right parenthesis space equals space 260
(ii) English newspaper          = <pre>uncaught exception: <b>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</b><br /><br />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<br />#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>
(iii) Hindi newspapers only    =     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 straight A minus straight B right parenthesis space equals space straight n left parenthesis straight A right parenthesis space minus straight n left parenthesis straight A intersection straight B right parenthesis space equals space 750 space minus 260 space equals space 490
         

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