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Relations and Functions

Short Answer Type

51.

Determine the domain and range of the relation defined as :

$space space space space space space space space space space space straight R space equals space left curly bracket left parenthesis straight x comma space straight y right parenthesis space colon space straight x element of straight N comma space straight y element of straight N comma space straight x less than 5 comma space straight y space equals space 3 straight x space plus space 1 right curly bracket$

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52.

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by aRb = {(a, b) : a, $straight b element of straight A$ , a divide b}. determine its domain and range.

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53. Let A = {2, 3, 4, 5}, which of the following relations from A into A is a function? If it is a function, determine the domain and range.

(i) {(2, 3), (2, 4), (2, 5)} (ii) {(2, 2), (3, 3), (4, 5), (5, 3)}

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54.
Let A = {2, 3, 4, 5}, which of the following relations from A into A is a function ? If it is a function, determine the domain and range.

(a) {(2,2), (3, 2), (4,2), (5,2)} (b) {(2, 3), (3,4),(4,5),(3,5)}

(a) x =2, 3, 4, 5

Thesen are all distinct values and each $straight x element of straight A$ has an image.

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

D_f= {2, 3, 4, 5}

R_f= {2}

(b) {(2, 3), (3,4),(4,5),(3,5)}

x =2, 3, 4, 5

These are all distinct values and each $straight x element of straight A$ has an image.

$rightwards double arrow$ Each $straight x element of straight A$ has a unique image.

∴ the set represents a function.