Login/Sign Up
CBSE Class 11 NCERT Exemplar Maths Relations and Functions
Relations and Functions

Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is (A) symmetric but not transitive (B) transitive but not symmetric (C) neither symmetric nor transitive (D) both symmetric and transitive

, , , , ,

The correct option is (B) transitive but not symmetric Given aRb ⇒ a is brother of b. This does not mean b is also a brother of a as b can be a sister of a. Therefore, R is not symmetric. aRb ⇒ a is...

read more

. Let \[\mathbf{A}\text{ }=\text{ }\left\{ \mathbf{1},\text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\ldots \text{ }\mathbf{9} \right\}\] and R be the relation in A ×A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in \[A\text{ }\times A\]. Prove that R is an equivalence relation and also obtain the equivalent class \[\left[ \left( \mathbf{2},\text{ }\mathbf{5} \right) \right]\].

, , , , ,

Given, \[\mathbf{A}\text{ }=\text{ }\left\{ \mathbf{1},\text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\ldots \text{ }\mathbf{9} \right\}\]and (a, b) R (c, d) if a + d = b + c for \[\left( a,\text{ }b...

read more

Let R be relation defined on the set of natural number N as follows: \[\mathbf{R}\text{ }=\text{ }\{\left( \mathbf{x},\text{ }\mathbf{y} \right):\text{ }\mathbf{x}\in \mathbf{N},\text{ }\mathbf{y}\in \mathbf{N},\text{ }\mathbf{2x}\text{ }+\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{41}\}\]. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

, , , , ,

Given function: \[\mathbf{R}\text{ }=\text{ }\{\left( \mathbf{x},\text{ }\mathbf{y} \right):\text{ }\mathbf{x}\in \mathbf{N},\text{ }\mathbf{y}\in \mathbf{N},\text{ }\mathbf{2x}\text{ }+\text{...

read more

. If A = \[\left\{ \mathbf{1},\text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{4}\text{ } \right\}\],define relations on A which have properties of being: (a) reflexive, transitive but not symmetric (b) symmetric but neither reflexive nor transitive (c) reflexive, symmetric and transitive.

, , , , ,

According to the question, \[A\text{ }=\text{ }\left\{ 1,\text{ }2,\text{ }3 \right\}\]. (i) Let \[{{R}_{1}}~=\text{ }\left\{ \left( 1,\text{ }1 \right),\text{ }\left( 1,\text{ }2 \right),\text{...

read more