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NCERT Class 11 - Math

Parvin Sinclair, G.P. Dikshit

Chapter 2

Relations and Functions - all with Video Answers

Educators

Section 1

Introduction

01:33

Problem 1

$$
\text { If }\left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right), \text { find the values of } x \text { and } y \text { . }
$$

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
02:01

Problem 2

$$
\text { If the set } \mathrm{A} \text { has } 3 \text { elements and the set } \mathrm{B}=\{3,4,5\} \text { , then find the number of }
$$

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
02:24

Problem 3

$$
\text { If } \mathrm{G}=\{7,8\} \text { and } \mathrm{H}=\{5,4,2\}, \text { find } \overline{\mathrm{G}} \times \mathrm{H} \text { and } \mathrm{H} \times \mathrm{G} \text { . }
$$

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
05:01

Problem 4

State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.
(i) If $\mathrm{P}=\{m, n\}$ and $\mathrm{Q}=\{n, m\}$, then $\mathrm{P} \times \mathrm{Q}=\{(m, n),(n, m)\}$.
(ii) If $\mathrm{A}$ and $\mathrm{B}$ are non-empty sets, then $\mathrm{A} \times \mathrm{B}$ is a non-empty set of ordered pairs $(x, y)$ such that $x \in \mathrm{A}$ and $y \in \mathrm{B}$.
(iii) If $\mathrm{A}=\{1,2\}, \mathrm{B}=\{3,4\}$, then $\mathrm{A} \times(\mathrm{B} \cap \phi)=\phi$.

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
03:55

Problem 5

$$
\text { If } \mathrm{A}=\{-1,1\}, \text { find } \mathrm{A} \times \mathrm{A} \times \mathrm{A}
$$

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
01:17

Problem 6

$$
\text { If } \mathrm{A} \times \mathrm{B}=\{(a, x),(a, y),(b, x),(b, y)\} . \text { Find } \mathrm{A} \text { and } \mathrm{B} \text { . }
$$

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
06:11

Problem 7

Let $\mathrm{A}=\{1,2\}, \mathrm{B}=\{1,2,3,4\}, \mathrm{C}=\{5,6\}$ and $\mathrm{D}=\{5,6,7,8\} .$ Verify that
(i) $\mathrm{A} \times(\mathrm{B} \cap \mathrm{C})=(\mathrm{A} \times \mathrm{B}) \cap(\mathrm{A} \times \mathrm{C})$.
(ii) $\mathrm{A} \times \mathrm{C}$ is a subset of $\mathrm{B} \times \mathrm{D}$.

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
05:05

Problem 8

Let $A=\{1,2\}$ and $B=\{3,4\} .$ Write $A \times B$. How many subsets will $A \times B$ have? List them.

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
02:04

Problem 9

Let $\mathrm{A}$ and $\mathrm{B}$ be two sets such that $n(\mathrm{~A})=3$ and $n(\mathrm{~B})=2 .$ If $(x, 1),(y, 2),(z, 1)$ are in $\mathrm{A} \times \mathrm{B}$, find $\mathrm{A}$ and $\mathrm{B}$, where $x, y$ and $z$ are distinct elements.

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
03:24

Problem 10

The Cartesian product $\mathrm{A} \times \mathrm{A}$ has 9 elements among which are found $(-1,0)$ and $(0,1)$. Find the set $A$ and the remaining elements of $A \times A$.

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator