Relations and Functions

Relations and Functions

Question

De-Morgan’s Laws : 



space space space space space space space space left parenthesis straight A space intersection space straight B right parenthesis apostrophe space space equals space straight A apostrophe space union space straight B apostrophe


Answer
space space space space space space space Let space straight x element of left parenthesis straight A intersection straight B right parenthesis apostrophe space be space any space arbitary space element.
<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 rightwards double arrow space space space space space space space space space space space space space straight x element of straight A apostrophe space space or space straight x space element of straight B apostrophe space space space space space space space space space space rightwards double arrow space space space space space space space space straight x element of left parenthesis straight A apostrophe union space straight B apostrophe right parenthesis 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 space space space left parenthesis straight A intersection straight B right parenthesis apostrophe space bottom enclose subset of space straight A apostrophe space union space straight B apostrophe space be space any space arbitary space element.                                ....(i)
Again, space space space let space straight x space element of space straight A apostrophe space union space straight B apostrophe
<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 space space space space space rightwards double arrow space space space space space straight x not an element of space left parenthesis straight A space intersection space straight B right parenthesis space space space space space space space space rightwards double arrow space space space space straight x space not an element of space left parenthesis straight A space intersection space straight B right parenthesis apostrophe

∴    space space space space space space straight A apostrophe space union space straight B apostrophe space space bottom enclose subset of space left parenthesis straight A space intersection space straight B right parenthesis apostrophe
From (i) and (ii), we have 
  space space space space space space space space space space open parentheses straight A space intersection space straight B close parentheses apostrophe space space space space equals space straight A apostrophe space union space straight B apostrophe


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