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Set A = (p, w, r, s), B = (l, p, m, q), Find : (a) A -B (b) B - A $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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103.

If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?

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104.

Let X {David, Gokul, Ram} be the set of students of class XI who are in the school hockey team. Let Y = {Shyam, David, Geet} be the set of students of class XI who are in the school football team.

(a) Find X ∪; Y and interpret the set.

(b) Find X ∩ Y and interpret the set.

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105.

Find the (a) Union (b) Intersection of the following pair of sets :

$space space space space space space space space space space space space space straight A space equals space left curly bracket space straight x space colon space straight x space element of straight N space and space straight x space is space straight a space multiple space of space 3 right curly bracket comma space straight B space equals space left curly bracket straight x space colon space straight x space element of space straight N comma space straight x space less than space 6 right curly bracket$

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106. Involution law :(A')' = A

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107.

Complement laws :

$space space space space space space space space left parenthesis straight i right parenthesis space straight A space intersection space straight A apostrophe space space equals space straight ϕ space space space space space space left parenthesis ii right parenthesis space space space straight A space union space straight A apostrophe space equals straight U$

$space space space space space space left parenthesis iii right parenthesis space straight ϕ apostrophe space equals space straight U space space space left parenthesis iv right parenthesis space space straight U apostrophe space equals space straight ϕ$

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108. De-Morgan’s Laws :

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

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109. De-Morgan’s Laws :

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

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.

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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

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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

$space space space space space space space space space space open parentheses straight A space intersection space straight B close parentheses apostrophe space space space space equals space straight A apostrophe space union space straight B apostrophe$