Relations and Functions

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New answer posted•a year ago

Relations and Functions Maths NCERT Exemplar Solutions Class 12th Chapter One

Let $A = {1, 2, 3, \dots, n}$ and $B = {a, b}$ . Then the number of surjections from $A$ into $B$ is

(A) ⁿp₂

(B) $2^{n} - 2$

(C) $2^{n} - 1$

(D) None of these

7 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol:

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New answer posted•a year ago

Relations and Functions Maths NCERT Exemplar Solutions Class 12th Chapter One

If the set $A$ contains 5 elements and the set $B$ contains 6 elements, then the number of one-one and onto mappings from $A$ to $B$ is

(A) 720

(B) 120

(C) 0

(D) None of these

2 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} I f A a n d B s e t s h a v e m a n d n e l e m e n t s r e s p e c t i v e l y, \\ t h e n t h e n u m b e r o f o n e - o n e a n d o n t o m a p p i n g f r o m A t o B i s \\ n! i f m = n \\ a n d 0 i f m \neq n \\ H e r e, m = 5 a n d n = 6 \\ 5 \neq 6 \\ S o, N u m b e r o f m a p p i n g = 0 \\ H e n c e, t h e c o r r e c t a n s w e r i s (c) \end{array}$

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New answer posted•a year ago

Relations and Functions Maths NCERT Exemplar Solutions Class 12th Chapter One

**The identity element for the binary operation $$ defined on $Q ~ {0}$ as $a b = \frac{a b}{2} \forall a, b \in Q ~ {0}$ is

(A) 1

(B) 0

(C) 2

(D)** None of these

4 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : a * b = \frac{a b}{2} \forall a, b \in Q - {0} \\ L e t e b e t h e i d e n t i t y e l e m e n t \\ ∴ a * e = \frac{a e}{2} = a \Rightarrow e = 2 \\ H e n c e, t h e c o r r e c t a n s w e r i s (c) . \end{array}$

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New answer posted•a year ago

Relations and Functions Maths NCERT Exemplar Solutions Class 12th Chapter One

Let $A = {1, 2, 3}$ and consider the relation

$R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}$ .

Then $R$ is

(A) Reflexive but not symmetric

(B) Reflexive but not transitive

(C) Symmetric and transitive

(D) Neither symmetric, nor transitive

3 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : A = {1, 2, 3} \\ a n d R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} \\ H e r e, 1 R 1, 2 R 2 a n d 3 R 3, S o, R i s r e f l e x i v e . \\ 1 R 2 b u t 2 R 1 o r 2 R 3 b u t 3 R 2, \\ S o, R i s n o t s y m m e t r i c . \\ 1 R 1 a n d 1 R 2 \Rightarrow 1 R 3, S o, R i s t r a n s i t i v e . \\ H e n c e, t h e c o r r e c t a n s w e r i s (a) . \end{array}$

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New answer posted•a year ago

Relations and Functions Maths NCERT Exemplar Solutions Class 12th Chapter One

Let us define a relation $R$ in $R$ as $a R b$ if $a \geq b$ . Then $R$ is:

(A) An equivalence relation

(B) Reflexive, transitive but not symmetric

(C) Symmetric, transitive but not reflexive

(D) Neither transitive nor reflexive but symmetric

5 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} H e r e, a R b i f a \geq b \\ \Rightarrow a R a \Rightarrow a \geq a w h i c h i s t r u e, s o i t i s r e f l e x i v e . \\ L e t a R b \Rightarrow a \geq b, b u t b \geq a, s o b R a \\ R i s n o t s y m m e t r i c . \\ N o w, a \geq b, b \geq c, \Rightarrow a \geq c, w h i c h i s t r u e . \\ S o, R i s t r a n s i t i v e . \\ H e n c e, c o r r e c t a n s w e r i s (b) . \end{array}$

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New answer posted•a year ago

Relations and Functions Class 12th

If a relation $R$ on the set ${1, 2, 3}$ be defined by $R = {(1, 2)}$ , then $R$ is

(A) Reflexive

(B) Transitive

(C) Symmetric

(D) None of these.

5 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : R = {(1, 2)} \\ a R a, ? ? s o i t i s n o t r e f l e x i v e . \\ a R b b u t b R a, s o i t i s n o t s y m m e t y r i c . \\ a R b a n d b R c \Rightarrow a R c w h i c h i s t r u e . \\ S o, R i s t r a n s i t i v e . \\ H e n c e, c o r r e c t a n s w e r i s (b) . \end{array}$

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New answer posted•a year ago

Relations and Functions Maths NCERT Exemplar Solutions Class 12th Chapter One

The maximum number of equivalence relations on the set $A = {1, 2, 3}$ are

(A) 1

(B) 2

(C) 3

(D) 5

6 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} H e r e, A = {1, 2, 3} \\ T h e n u m b e r o f e q u i v a l e n c e r e l a t i o n s a r e a s f o l l o w s : \\ R_{1} = {(1, 1), (1, 2), (2, 1), (2, 3), (1, 3)} \\ R_{2} = {(2, 2), (1, 3), (3, 1), (3, 2), (1, 2)} \\ R_{3} = {(3, 3), (1, 2), (2, 3), (1, 3), (3, 2)} \\ H e n c e, c o r r e c t a n s w e r i s (d) \end{array}$

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New question posted•a year ago

Relations and Functions Maths NCERT Exemplar Solutions Class 12th Chapter One

The maximum number of equivalence relations on the set <math><mrow><mi>A</mi><mo>=</mo><mrow><mo>{</mo><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow><mo>}</mo></mrow></mrow></math> are (A) 1 (B) 2 (C) 3 (D) 5

5 Views|Posted a year ago

Asked by Alok Kumar Singh

New answer posted•a year ago

Relations and Functions Maths NCERT Exemplar Solutions Class 12th Chapter One

Consider the non-empty set consisting of children in a family and a relation $R$ defined as $a R b$ if $a$ is the 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.

7 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} H e r e, a R b \Rightarrow a i s a b r o t h e r o f b . \\ a R a \Rightarrow a i s a b r o t h e r o f a w h i c h i s n o t t r u e . \\ S o, R i s n o t r e f l e x i v e . \\ a R b \Rightarrow a i s a b r o t h e r o f b . \\ b R a \Rightarrow w h i c h i s n o t t r u e b e c a u s e b m a y b e s i s t e r o f a . \\ \Rightarrow a R b \neq b R a \\ S o, R i s n o t s y m m e t r i c . \\ N o w, a R b, b R c \Rightarrow a R c \\ \Rightarrow a i s t h e b r o t h e r o f b a n d b i s t h e b r o t h e r o f c . \\ ∴ a i s a l s o t h e b r o t h e r o f c . \end{array}$

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New answer posted•a year ago

Relations and Functions Maths NCERT Exemplar Solutions Class 12th Chapter One

Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $a R b$ if $a$ is congruent to $b \forall a, b \in T$ . Then $R$ is:

(A) Reflexive but not transitive

(B) Transitive but not symmetric

(C) Equivalence

(D) None of these.

5 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Objective Type Question as classified in NCERT Exemplar

Sol: $\begin{array}{l} \end{array}$

$\begin{array}{l} I f a = b \forall a, b \in T \\ t h e n a R a \Rightarrow a ≅ a w h i c h i s t r u e f o r a l l a \in T \\ S o, R i s r e f l e x i v e \\ N o w, a R b a n d b R a . \\ i . e ., a ≅ b a n d b ≅ a w h i c h i s t r u e f o r a l l a \in T \\ R i s s y m m e t r i c . \\ L e t a R b a n d b R c . \\ \Rightarrow a ≅ b a n d b ≅ a \Rightarrow a ≅ c \forall a, b, c \in T \\ S o, R i s t r a n s i t i v e . \\ H e n c e, R i s e q u i v a l e n c e r e l a t i o n . \\ S o, t h e c o r r e c t a n s w e r i s (c) . \end{array}$

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