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Question
State, if the following pair of a set is equal or not:
E = {x : x 2 + 8x - 9 = 0} and F = {1, - 9}
Solution
E = {x : x2 + 8x − 9 = 0}
x2 + 8x − 9 = 0
⇒ x2 + 9x − x − 9 = 0
⇒ x(x+9) − 1(x+ 9) = 0
⇒ (x−1) (x+9) = 0
∴ Either x + 9 = 0
⇒ x = −9
Or
x − 1 = 0
⇒ x = 1
∴ E = {−9, 1}
F = {1, −9}
Now we see that the elements of sets E and F are the same (identical)
Sets E and F are equal.
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