Which of the following are pairs of equal sets?

Question:

Which of the following are pairs of equal sets?

$J=\{2,3\}$ and $K=\left\{x: x \in Z,\left(x^{2}+5 x+6\right)=0\right\}$

 

Solution:

Equal Sets = Two sets A and B are said to be equal if they have exactly the

same elements & we write A = B

We have,

$J=\{2,3\}$

and $K=\left\{x: x \in Z,\left(x^{2}+5 x+6\right)=0\right\}$

Here, $x \in Z$ and $x^{2}+5 x+6=0$

The given equation can be solved as:

$x^{2}+5 x+6=0$

$\Rightarrow x^{2}+2 x+3 x+6=0$

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

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

$\Rightarrow x=-2$ and $-3$

$\therefore K=\{-2,-3\}$

∴ J ≠ K because elements of both the sets are not equal.

 

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