Question

If $R=\left\{\right(x,y):3x+2y=15\text{and}x,y\in N\}$, the range of the relation R is .........

• A. $\{1,2\}$
• B. $\{1,2,...,5\}$
• C. $\{1,2,...,7\}$
• D. $\{3,6\}$

Answer 1

Answer: (D)

$\{3,6\}$

Since x and y belong to natural numbers we need to find positive integral solutions for $3x+2y=15$

$2y=15-3x$

$\Rightarrow y=\frac{15-3x}{2}$

For $x=0,2,4$ $y$ will become fractional which is not possible

For $x\ge 5$ y becomes 0 or negative which again is not possible.

Hence for $x=1,3$ y= 6,3$ respectively.

Hence the range is $\{3,6\}$