Question

Let $R$ be a relation in $N$ defined by $R=\left\{\right(1+x,1+x^2):x\le 5,xϵN\}$. Which of the following is false?

• A. $R=\left\{\right(2,2),(3,5),(4,10),(5,17),(6,26\left)\right\}$
• B. Domain of $R=\{2,3,4,5,6\}$
• C. Range of $R=\{2,5,10,17,26\}$
• D. at least one is false

Answer 1

Answer: (A), (B), (C)

The correct options are
A $R=\left\{\right(2,2),(3,5),(4,10),(5,17),(6,26\left)\right\}$
B Domain of $R=\{2,3,4,5,6\}$
C Range of $R=\{2,5,10,17,26\}$

$R=\left\{\right(1+1,1+1),(1+2,1+4),(1+3,1+9),(1+4,1+16),(1+5,1+25\left)\right\}$
$=\left\{\right(2,2),(3,5),(4,10),(5,17),(6,26\left)\right\}$
Domain of $R=\{x:(x,y\left)ϵR\right\}=\{2,3,4,5,6\}$
Range of $R=\{y:(x,y\left)ϵR\right\}=\{2,5,10,17,26\}$
$\therefore$ The correct answer is (a).