Question

Find the proper subsets of {x : x² – 9x – 10 = 0}

Answer 1

X² - 9x - 10 = 0
⇒ x² - 10x + x - 10 = 0
⇒ x(x-10)+1  (x-10) = 0
⇒ (x-10)(x+1) = 0
∴ Either x-10 = 0
⇒ x = 10
or
x+1 = 0
⇒ x = -1
Given set = {-1, 10}
Proper subsets of this set = φ, {-1}, {10}