Relations and Functions

Relations and Functions

Question

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Answer

Set  A = set of people who play cricket
Set B = set of people who play tennis
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 union straight B right parenthesis space equals space 65                                                                            ....(i)
                   
                   n(A)  = 40                                                                                   ....(ii)
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#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)
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#6 {main}</pre>                                                                              .....(iii)
Using,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 space 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
                     65 = 40 + n(B)  -10
rightwards double arrow     n(B) = 65 - 40 + 10 = 35
Hence, (a) Number of people who play tennis = n(B) = 35
Number of people who play tennis only = n(B-A)
                              space space space space space space space space space space space space space space space space space space space space space space space equals space straight n left parenthesis straight B right parenthesis space minus straight n left parenthesis straight A intersection straight B right parenthesis space equals space 35 minus 10 equals 25

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