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Relations and Functions

Short Answer Type

41.
Let R be a relation on set N of natural numbers defined by R = {(a, b) : a, b ∊ N, a + 3b = 12} (or a R b : a + 3b = 12).

Find (i) R in Roster form (ii) Domain of R (iii) Range of R.

The given relation is aRb : a + 3b = 12

$rightwards double arrow$ $space straight b space equals space fraction numerator 12 space minus straight a over denominator 3 end fraction$

When $space space space space space space space space space space straight a equals 1 comma space straight b equals 11 over 3 not an element of straight N$

$space space space space space space space space space space space space straight a equals 2 comma space straight b equals 10 over 3 not an element of straight N$

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...........................

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight a equals 6 comma space straight b equals 3 over 3 space equals space 2 space element of space straight N$
...................................

a = 9, $space space space space space space space space straight b equals 3 over 3 equals 1 element of straight N$

a = 10, $space space space space space space space space space space space space space space space space space space space space space space straight b equals 2 over 3 not an element of straight N$

a = 11, $space space space space space space space space space space straight b equals 1 third not an element of straight N$

For $space space space space space space straight a greater or equal than 12 comma space straight b space equals space 0 space or space minus space ve comma space not an element of space straight N$

Hence, R = {(3, 3), (6, 2), (9, 1)}

(ii) Domain of R = {3, 6, 9}

(iii) Range of R = {3, 2, 1}

643 Views

42. Let A = {1, 3, 5}, B = {7,11}. If R = {(a, b) : a ∊ A, b e B, a – b = odd}, then show that R is an empty relation.

120 Views

43. Determine the domain and range of a relation R defined by :

R = {(x + 1), (x + 5) : x = 0, 1, 2, 3, 4, 5}

210 Views

44.

Let R be the relation on Z defined by R = {(a,b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.

111 Views

45. Let R be a relation from N to N, defined by

space space space space space straight R space equals space left curly bracket left parenthesis straight a comma space straight b right parenthesis space colon space straight a comma space straight b space element of straight N space and space straight a space equals space straight b squared right curly bracket

. Are the following true?

left parenthesis straight i right parenthesis space left parenthesis straight a comma space straight a right parenthesis element of straight R space for space all space straight a element of straight N space

left parenthesis ii right parenthesis space left parenthesis straight a comma space straight b right parenthesis element of straight R rightwards double arrow left parenthesis straight b comma straight a right parenthesis element of straight R

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108 Views

46.

Let R be a relation from Q to Q defined by :

$space space space space space space space space space space space space space space space space straight R space equals space left curly bracket left parenthesis straight a comma space straight b right parenthesis space colon straight a element of straight Q comma space straight b element of straight Q comma space straight a minus straight b element of straight Z$

Show that

$space space space space space space left parenthesis straight i right parenthesis space left parenthesis straight a comma space straight a right parenthesis element of straight R for all straight a element of straight Q$

$space space space space space space left parenthesis ii right parenthesis space left parenthesis straight a comma space straight b right parenthesis element of straight R rightwards double arrow left parenthesis straight b comma straight a right parenthesis element of straight R$

133 Views

47.

Determine the domain and range of relation :

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

(b) R = $space space space space left curly bracket left parenthesis straight x comma space straight y right parenthesis space colon space straight x element of straight N comma space 3 less than straight x less than 7 comma space straight y space equals 3 right curly bracket$

112 Views

48. If the relation R is defined by R = {(2x + 1, 2x) : x = 0, 1, 2, 3, 4, 5}, then find domain and range of R.

122 Views

49.

Write the relation : R {(2x+1, x²-1) : x is an odd prime number less than 10} in Roster form.

134 Views

50.

Let A = {a, b} and B = {1, 2}. How many relations are three from set A into set B? write all the relations.

121 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

41. Let R be a relation on set N of natural numbers defined by R = {(a, b) : a, b ∊ N, a + 3b = 12} (or a R b : a + 3b = 12). Find (i) R in Roster form (ii) Domain of R (iii) Range of R.

41.
Let R be a relation on set N of natural numbers defined by R = {(a, b) : a, b ∊ N, a + 3b = 12} (or a R b : a + 3b = 12).

Find (i) R in Roster form (ii) Domain of R (iii) Range of R.