Question

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

• A. $\left\{(1,4),(2,5),(3,6),\dots \right\}$
• B. $\left\{(4,1),(5,2),(6,3),..\right\}$
• C. $\left\{(1,3),(2,6),(3,9),\dots \right\}$
• D. None of the above

Answer 1

The correct option is B

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

Explanation for correct option

Option(B): Given: A relation $\mathrm{R}$ defined on the set as $\mathrm{\{}(\mathrm{a},\mathrm{b}):\mathrm{a}$ differs from $\mathrm{b}$ by $3\}$

$\Rightarrow \mathrm{a}-\mathrm{b}=3$

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

Now, for $\mathrm{a}=4$ and $\mathrm{b}=1$

$\Rightarrow 4-1=3$

For $\mathrm{a}=5$, $\mathrm{b}=2$

$\Rightarrow 5-2=3$

For $\mathrm{a}=6$, $\mathrm{b}=3$

$\Rightarrow 6-3=3$

Thus option(B) is correct

Explanation for incorrect options

Option (A): $\left\{(1,4),(2,5),(3,6),\dots \right\}$

Now, for $\mathrm{a}=1$ and $\mathrm{b}=4$

$\Rightarrow 1-4=-3\ne 3$

For $\mathrm{a}=2$, $\mathrm{b}=5$

$\Rightarrow 2-5=-3\ne 3$

For $\mathrm{a}=3$, $\mathrm{b}=6$

$\Rightarrow 3-6=-3\ne 3$

Thus option(A) is incorrect

Option (C): $\left\{(1,3),(2,6),(3,9),\dots \right\}$

Now, for $\mathrm{a}=1$ and $\mathrm{b}=3$

$\Rightarrow 1-3=-2\ne 3$

For $\mathrm{a}=2$, $\mathrm{b}=6$

$\Rightarrow 2-6=-4\ne 3$

For $\mathrm{a}=3$, $\mathrm{b}=9$

$\Rightarrow 3-9=-6\ne 3$

Thus option(C) is incorrect

Hence, the correct option is option(B) i.e. $\left\{(4,1),(5,2),(6,3),..\right\}$