Prove that :   from Mathematics Sets
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    Sets

    Multiple Choice QuestionsShort Answer Type

    121. Show that :

    space space space space space space space straight A union left parenthesis straight B minus straight A right parenthesis space equals space straight A union straight B
    114 Views
    Answer
    122.

    If U = {a, b, c, d, e, f, g, h, k}, A = {a, b, c, d), B  = {b, d, f, h}, C = {c, d, e, f} find 

    (a) B'     (b)   C'        space space space space space space space space space space space space left parenthesis straight c right parenthesis space space space left parenthesis straight A union straight B right parenthesis apostrophe space space space space space space space space space space space space space left parenthesis straight d right parenthesis space open parentheses straight B union straight C close parentheses apostrophe space space space space space space space space  (e)   (B - C)'
    124 Views
    Answer
    123.

    Find the following to make them true statements :


    space space space space space space space space space left parenthesis straight a right parenthesis space space left parenthesis straight ϕ apostrophe right parenthesis apostrophe intersection straight A space equals space...... space space left parenthesis straight b right parenthesis space left parenthesis straight U apostrophe right parenthesis apostrophe union straight A space equals space....... space space space space space left parenthesis straight c right parenthesis space left parenthesis straight A intersection straight B right parenthesis apostrophe space equals space.......

    space space space space space space space space space space space left parenthesis straight d right parenthesis space open parentheses straight A intersection straight ϕ close parentheses apostrophe space equals space....... space space space space space space left parenthesis straight e right parenthesis space open parentheses straight A union straight A apostrophe close parentheses apostrophe equals space......... space space space space space left parenthesis straight f right parenthesis space open parentheses straight A intersection straight A apostrophe close parentheses apostrophe space equals space.......... space space space space space space space

    127 Views
    Answer
    124. If A and B are two sets, then

    space space space space space space left parenthesis straight i right parenthesis space straight n left parenthesis straight A minus straight B right parenthesis space equals space straight n left parenthesis straight a right parenthesis minus straight n left parenthesis straight A intersection straight B right parenthesis          
    122 Views
    Answer
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    125.

    Prove that :  space space space space space straight n left parenthesis straight A increment straight B right parenthesis space equals straight n left parenthesis straight A right parenthesis space plus space straight n left parenthesis straight B right parenthesis minus 2 straight n space left parenthesis straight A intersection straight B right parenthesis

    We know that

    space space space space space space space space space space space space space space space space space space straight A increment straight B space equals space left parenthesis straight A minus straight B right parenthesis space union space left parenthesis straight B minus straight A right parenthesis

    space space space space space space space space straight n left parenthesis straight A increment straight B right parenthesis space equals space straight n open square brackets open parentheses straight A minus straight B close parentheses space union space left parenthesis straight B minus straight A right parenthesis close square brackets equals space straight N left parenthesis straight A minus straight B right parenthesis space plus space straight n left parenthesis straight B minus straight A right parenthesis
                
                                                                                                 [∵ A-B and B-A are disjoint sets ]

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          <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>


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    126.

    If A, B and C be three sets, then

    space space space space space space space space space space space space space space space straight n left parenthesis straight A union straight B union straight V right parenthesis space equals space straight n left parenthesis straight A right parenthesis space plus straight n left parenthesis straight B right parenthesis space plus straight n left parenthesis straight C right parenthesis space minus straight n left parenthesis straight A intersection straight B right parenthesis minus straight n left parenthesis straight B intersection straight C right parenthesis minus straight n left parenthesis straight C intersection straight A right parenthesis plus straight n left parenthesis straight A intersection straight B intersection straight C right parenthesis

    122 Views
    Answer
    127.

    In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

    160 Views
    Answer
    128.  X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and (X ∩ Y) has 10 elements. How many elements does Y have?
    123 Views
    Answer
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    129.

    In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

    125 Views
    Answer
    130. In a group of people, 50 speak both English and Hindi and 30 speak English but not Hindi. If all the people speak at least one of the two languages, how many speak English?
    655 Views
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