Are following pair of sets equal ? Give reasons. A = { 2,3} ,quad ,,,B = { x:x is solution of {x^2}

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1.Set Theory

easy

Are the following pair of sets equal ? Give reasons.

$A = \{ 2,3\} ,\quad \,\,\,B = \{ x:x$ is solution of ${x^2} + 5x + 6 = 0\} $

Option A

Option B

Option C

Option D

Solution

$A = \{ 2,3\} ,\quad \,\,\,B = \{ x:x$ is solution of ${x^2} + 5x + 6 = 0\} $

The equation $x^{2}+5 x+6=0$ can be solved as:

$x(x+3)+2(x+3)=0$

$(x+2)(x+3)=0$

$x=-2$ or $x=-3$

$\therefore A=\{2,3\} ; B=\{-2,-3\}$

$\therefore A \neq B$

Standard 11

Mathematics

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