Question

Are the sets A = {4, 5, 6} and B = {x : x² – 5x – 6 = 0} disjoint?

Answer 1

A = {4, 5, 6} 

B = {x : x² - 5x - 6 = 0}

x² - 5x - 6 = 0

⇒ x² - 6x + x -6 = 0

⇒ x(x - 6) +1(x - 6) = 0

⇒ (x - 6) (x+1) = 0

∴ Either x - 6 = 0x

⇒ x = 6

Or 

x+1 = 0

⇒ x = -1

∴ B = {6, -1}

Hence set A and set B are not disjoint because these sets have element 6 in common.