Question

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

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

Answer 1

Answer: (C), (D)

The correct options are
C Domain of $S=\{1,2,4,6,8\}$
D Range of $S=\{1,2,3,4,5\}$

As per definition of $S$
$S=\left\{\right(x,y):x+2y=10,1\le x,y\le 10,x,y\in N\}\Rightarrow S=\left\{\right(2,4),(4,3),(6,2),(8,1\left)\right\}$