Let A={x, y, z} and B={1,2} . number of relations from A to B .

English

Gujarati

Hindi

2.Relations and Functions

easy

Let $A=\{x, y, z\}$ and $B=\{1,2\} .$ Find the number of relations from $A$ to $B$.

A

$2^{6}$

B

$2^{6}$

C

$2^{6}$

D

$2^{6}$

Solution

It is given that $A=\{x, y, z\}$ and $B=\{1,2\}$

$\therefore A \times B=\{(x, 1),(x, 2),(y, 1),(y, 2),(z, 1),(z, 2)\}$

Since $n(A \times B)=6,$ the number of subsets of $A \times B$ is $2^{6}$

Therefore, the number of relations from $A$ to $B$ is $2^{6}$.

Standard 11

Mathematics

Share

Similar Questions

Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$

Write down the domain, codomain and range of $R .$

easy

Let $R$ be a relation from $N$ to $N$ defined by $R =\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} .$ Are the following true?

$(a, a) \in R ,$ for all $a \in N$

easy

Let $A=\{1,2,3,4,6\} .$ Let $R$ be the relation on $A$ defined by $\{ (a,b):a,b \in A,b$ is exactly divisible by $a\} $

Write $R$ in roster form

easy

Let $A=\{1,2,3, \ldots, 14\} .$ Define a relation $R$ from $A$ to $A$ by $R = \{ (x,y):3x – y = 0,$ where $x,y \in A\} .$ Write down its domain, codomain and range.

easy

The relation $R$ defined on the set of natural numbers as $\{(a, b) : a$ differs from $b$ by $3\}$, is given by

easy