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Equal Sets

State the fol...

Question

State the following pair of sets are equal or not.
If they are equal then write $1$ , else $0$ .
E = { $x$ : $x^{2} + 8 x - 9 = 0$ } and F = { $1, - 9$ }.

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Solution

Two sets are equal if they have exactly the same elements.
For Set E,
$x^{2} + 8 x - 9 = 0$
$\Rightarrow x^{2} + 9 x - x - 9 = 0$
$\Rightarrow (x + 9) - (x + 9) = 0$
$\Rightarrow (x + 9) (x - 1) = 0$
$\Rightarrow x = 1, - 9$
Hence, $E = {1, - 9}$
Since sets E and F have the same elements, they are equal sets.

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