Relations and Functions

Relations and Functions

Question

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

Answer
<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>
                     
   space space space space space space space space space space equals space straight n left parenthesis straight A right parenthesis space plus straight n left parenthesis straight B right parenthesis space minus space straight n left parenthesis straight A intersection straight B right parenthesis plus straight n left parenthesis straight C right parenthesis minus straight n left square bracket left parenthesis straight A intersection straight C right parenthesis union left parenthesis straight B intersection straight C right parenthesis right square bracket

space space space space space space space space space space space space space space equals space space 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 plus straight n left parenthesis straight C right parenthesis space minus straight n left square bracket left parenthesis straight A intersection straight C right parenthesis plus straight n left parenthesis straight B intersection straight C right parenthesis minus straight n left curly bracket left parenthesis straight A intersection straight C right parenthesis intersection left parenthesis straight B intersection straight C right parenthesis right square bracket
space space space space space space space space space space space space space space equals space 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 space minus straight n left parenthesis straight A intersection straight C right parenthesis minus straight n left parenthesis straight B intersection straight C right parenthesis plus straight n left parenthesis straight A intersection straight B intersection straight C right parenthesis

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