Question

Let $A$ be the set of first $10$ natural numbers and $R$ be a relation on $A$ defined by $(x,y)\in R\iff x+2y=10.$ Then the range of $R$ is

• A. $\{1,2,3,\dots ,10\}$
• B. $\{2,4,6,8\}$
• C. $\{2,4,6,8,10\}$
• D. $\{1,2,3,4\}$

Answer 1

The correct option is D $\{1,2,3,4\}$

$y=\frac{10-x}{2}$
$y\in N\Rightarrow x$ should be even number.
So, Domain $=\{2,4,6,8\}$
$\Rightarrow$ Range $=\{4,3,2,1\}$