Question

If A $=${$x:x^2-3x+2=0$}, and $R$ is a universal relation on $A$, then $R$ is

• A. $\left\{\right(1,1),(2,2\left)\right\}$
• B. $\left\{\right(1,1\left)\right\}$
• C. $\varphi$
• D. $\left\{\right(1,1),(1,2\left)\right(2,1),(2,2\left)\right\}$

Answer 1

Answer: (D)

$\left\{\right(1,1),(1,2\left)\right(2,1),(2,2\left)\right\}$

Consider, $x^2-3x+2=0$
$⟹x^2-2x-x+2=0$
$⟹(x-2)(x-1)=0$
$⟹x=1,2$

$\therefore A=\{1,2\}$
Also R is universal relation on set A, then every element of set A is related every other element of A

So $R=\left\{\right(1,1),(1,2),(2,1),(2,2\left)\right\}$.