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Sets

Short Answer Type

111.

Let U ={1,2,3,4,5,6,7,8,9}

A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6}

Find (a) A' (b) B' (c)(A ∪ C)' (d) (A ∪ B)' (e) (A')' (f) (B-C)'

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112.
Fill in the blanks to make each of the following a true statement : (i) A ∪ A′ = . . . (ii) φ′ ∩ A = . . . (iii) A ∩ A′ = . . . (iv) U′ ∩ A = . . .

(a) A ∪ A′ = U [By complement law]

(b) φ′ ∩ A = U ∪ A = A [By complement law]

(c) A ∩ A' = φ [By complement law]

(d) U′ ∩ A = φ′ ∩ A = φ [By complement law]

111 Views

113.

Id U = {1, 2, 3, 4, 5, 7, 8, 9}, A = {2, 4, 6, 8} , B ={2, 3, 5, 7} verify De Morgan's laws:

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

122 Views

114. Let U be the set of all triangles in a plane. If A is set of all triangles with at least one angle different from 60°, what is A'.

150 Views

Long Answer Type

115.

Taking the set of natural numbers as the universal set, write down the complements of the following sets :

(i) {x : x is an even natural number} (ii) {x : x is an odd natural number}

(iii) {x : x is a positive multiple of 3} (iv) {x : x is a prime number}

(v) {x : x is a natural number divisible by 3 and 5}

(vi) {x : x is a perfect square} (vii) {x : x is a perfect cube}

(viii) { x : x + 5 = 8 } (ix) { x : 2x + 5 = 9}

(x) { x : x ≥ 7 } (xi) {x : x ∈ N and 2x + 1 > 10}

159 Views

Short Answer Type

116.

Prove that : $space space space space space space space space space space space space space space space space space space space straight A space bottom enclose subset of space straight B space left right double arrow straight B apostrophe space bottom enclose subset of space straight A apostrophe space$

or $space space space space space space space space space space space space space space space space space space space straight A space bottom enclose subset of space straight B space space space if space space straight B apostrophe space bottom enclose subset of space straight A apostrophe space$