Question

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

$B=\{y:y\text{is a letter in the word WOLF}\}$

Answer 1

(i) $A=\{2,3\}$

$B=\{x:x\text{is a solution of}{x}^2+5x+6=0\}$
$x^2+5x+6=0$
$x(x+3)+2(x+3)=0$
$(x+2)(x+3)=0$
$x=-2$ or $x=-3$
$\therefore B=\{-2,-3\}$
$\therefore A\ne B$
(ii) $A=\{x:x\text{is a letter in the word}FOLLOW\}=\{F,O,L,W\}$
$B=\{y:y\text{is a letter in the word WOLF}\}=\{W,O,L,F\}$
The order in which the elements of a set are listed is not significant.
$\therefore A=B$