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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

CBSE, Class 12, Exercise 1, Maths, NCERT Exemplar, Relations and Functions

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...

. 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
$\left[ \left( \mathbf{2},\text{ }\mathbf{5} \right) \right]$
.

CBSE, Class 12, Exercise 1, Maths, NCERT Exemplar, Relations and Functions

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...

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.

CBSE, Class 12, Exercise 1, Maths, NCERT Exemplar, Relations and Functions

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{...

. 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.

CBSE, Class 12, Exercise 1, Maths, NCERT Exemplar, Relations and Functions

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{...

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

. 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.

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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

. Let 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 . Prove that R is an equivalence relation and also obtain the equivalent class .

Let R be relation defined on the set of natural number N as follows: . Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

. If A = ,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.

. 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.