Question

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

• A. $\left\{(1,4),(2,5),(3,6)...\right\}$
• B. $\left\{(4,1),(5,2),(6,3),...\right\}$
• C. $\left\{(1,3),(2,6),(1,3),...\right\}$
• D. None of the above

Answer 1

The correct option is B

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

Explanation for the correct option:

Define the elements of the given relation.

Given: $a$ differs from $b$ by $3$

$$\begin{gathered} a–3=b \\ a=b+3 \end{gathered}$$

If $N=1,2,3,4\dots .$

$$\begin{gathered} b=1,a=4 \\ b=2,a=5 \\ b=3,a=6 \end{gathered}$$

Thus, the relation becomes $\left\{(4,1),(5,2),(6,3)\dots ..\right\}$.

Hence, option $B$ is the correct answer.