Relations and Functions

Relations and Functions

Question

In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

Answer

Set A = set of students who know Hindi
rightwards double arrow                n(A)  = 100                                                                                    .....(i)
Set B = set of students who know English
rightwards double arrow               n(B)   = 50                                                                                      ....(ii)
Also,    space space space space space space space space space space space space space space space space space space space straight n open parentheses straight A intersection straight B close parentheses space equals space 25                                                                        .....(iii)   
Using,  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 equals 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 comma space we space get
           space space space space space space space space space space straight n left parenthesis straight A union straight B right parenthesis  = 100 +50 - 25 = 125
All students know at least one of the two languages
   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 square bracket left parenthesis straight A union straight B right parenthesis apostrophe right curly bracket space equals space 0 space space space space space space space space space space space space space space space space space rightwards double arrow space space space space space straight n left parenthesis straight U right parenthesis minus straight n left parenthesis straight A union straight B right parenthesis equals 0
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#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>
Hence, the number of students in the group = 125

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