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Are the following pairs of sets equal? Gives reasons.
(i) $A=\{2,3\}, B=\left\{x: x\right.$ is solution of $\left.x^2+5 x+6=0\right\}$ $A=\{x: x$ is a letter in the word 'FOLLOW' $\}$
(ii) $B=\{y: y$ is a letter in the word 'WOLF' $\}$
(i) $A=\{2,3\}, B=\left\{x: x\right.$ is solution of $\left.x^2+5 x+6=0\right\}$ $A=\{x: x$ is a letter in the word 'FOLLOW' $\}$
(ii) $B=\{y: y$ is a letter in the word 'WOLF' $\}$
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Verified Answer
(i) $\mathrm{No}, A=\{2,3\}$
But solution of $x^2+5 x+6=0$
$\Rightarrow \quad x^2+3 x+2 x+6=0$
$\Rightarrow \quad x(x+3)+2(x+3)=0$
$\Rightarrow \quad(x+3)(x+2)=0$
$\Rightarrow \quad x+3=0$ or $x+2=0$
$\Rightarrow \quad x=-3$ or $x=-2$
$\Rightarrow \quad B=\{-2,-3\}$
Hence, $\mathrm{A} \neq \mathrm{B}$
(ii) Yes, $A=\{\mathrm{F}, \mathrm{O}, \mathrm{L}, \mathrm{W}\}$
and $B=\{\mathrm{W}, \mathrm{O}, \mathrm{L}, \mathrm{F}\}$
Hence, $A=B$
But solution of $x^2+5 x+6=0$
$\Rightarrow \quad x^2+3 x+2 x+6=0$
$\Rightarrow \quad x(x+3)+2(x+3)=0$
$\Rightarrow \quad(x+3)(x+2)=0$
$\Rightarrow \quad x+3=0$ or $x+2=0$
$\Rightarrow \quad x=-3$ or $x=-2$
$\Rightarrow \quad B=\{-2,-3\}$
Hence, $\mathrm{A} \neq \mathrm{B}$
(ii) Yes, $A=\{\mathrm{F}, \mathrm{O}, \mathrm{L}, \mathrm{W}\}$
and $B=\{\mathrm{W}, \mathrm{O}, \mathrm{L}, \mathrm{F}\}$
Hence, $A=B$
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