Question

Let $A=\{x:x<11,x\in N\}$. Let $R$ be a relation on $A$ defined by $(x,y)\in R$ if and only if $x+2y=10$. Which of the following is false?

• A. $R=\left\{\right(2,4),(4,3),(6,2),(8,1\left)\right\}$
• B. Domain of $R=\{1,2,4,6,8\}$
• C. Range of $R=\{1,2,3,4,5\}$
• D. Both (b) and (c)

Answer 1

The correct option is D Both (b) and (c)

As per definition of $R$,
$R=\left\{\right(x,y):x+2y=10,1\le x,y\le 10,x,y\in N\}\Rightarrow R=\left\{\right(2,4),(4,3),(6,2),(8,1\left)\right\}$
$\therefore$ Options $\left(b\right)$ and $\left(c\right)$ are incorrect.