Question

State, if the following pair of a set is equal or not:

E = {x : x ² + 8x - 9 = 0} and F = {1, - 9} 

Answer 1

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.