Question

Is {x : x² – 7x + 12 = 0} = {3, 4} ?

Answer 1

x² - 7x + 12 = 0
⇒ x² - 4x - 3x + 12 = 0
⇒ x (x - 4) - 3(x - 4) = 0
⇒ (x - 4) (x - 3) = 0
∴ Either x - 4 = 0 
⇒ x = 4
Or
x - 3 = 0
⇒ x = 3
∴ {x : x² - 7x + 12 = 0}
= {3, 4} is true.