Relation R defined on set of natural numbers as {(a, b) : a differs from b by 3} , is given by

English

Gujarati

Hindi

2.Relations and Functions

easy

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

A

$\{(1, 4, (2, 5), (3, 6),.....\}$

B

$\{(4, 1), (5, 2), (6, 3),.....\}$

C

$\{(1, 3), (2, 6), (3, 9),..\}$

D

None of these

Solution

(b) $R = \{ (a,\,b):a,\,b \in N,\,a – b = 3\} = \{ ((n + 3),n):n \in N\} $

$ = \{ (4,\,1),\,(5,\,2),\,(6,\,3),\,…..\} $.

Standard 11

Mathematics

Share

Similar Questions

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\} $

Find the domain 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?

$(a, b) \in R ,(b, c) \in R$ implies $(a, c) \in R$

easy

The Fig shows a relationship between the sets $P$ and $Q .$ Write this relation

in set-builder form

What is its domain and range?

easy

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

Depict this relation using an arrow diagram.

easy

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

easy