Question

Are the following pair of sets equal ? Give reasons.
$\left(i\right)A=\{2,3\},B=\{x:x$ is solution of $x^2+5x+6=0\}$
$\left(ii\right)A=\{x:x$ is a letter in the word $\text{Follow}\}$
$B=\{y:y$ is a letter in the word $\text{WOLF}\}$

Answer 1

$\left(i\right)$ Given:
$A=\{2,3\}$
$B=\{x:x$ is solution of $x^2+5x+6=0\}$
$x^2+5x+6=0$ can be written as,
$x^2+3x+2x+6=0$
$\Rightarrow x(x+3)+2(x+3)=0$
$\Rightarrow (x+2)(x+3)=0$
$\Rightarrow x=-2$ or $x=-3$
$\therefore B=\{-2,-3\}$
On comparing we get, $A\ne B$.

$\left(ii\right)A=\{x:x$ is a letter in the word $\text{Follow}\}$
$\therefore A=\{F,O,L,W\}$
$B=\{y:y$ is a letter in the word $\text{WOLF}\}$
$\therefore B=\{W,O,L,F\}$
Every element present in $A$ is also in $B$ and every element present in $B$ is also in $A$.
Order in which the elements of a set are listed, is not significant.
$\therefore A=B$.