Question

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

A = {x : x ∈ N, x < 3} and B = {y : y² - 3y + 2 = 0} 

Answer 1

A = {x : x ∈ N, x < 3}

= {1, 2}

B = {y : y² - 3y + 2 = 0}

y² - 3y + 2 = 0

⇒ y² - 2y - y + 2 = 0

⇒  y(y - 2) -1(y - 2) = 0

⇒  (y - 2)(y - 1) = 0

∴ Either y - 2 = 0

⇒  y = 2

Or

y - 1 = 0

⇒  y = 1

∴ B = {1, 2}

Now we see that elements of sets A and B are the same (identical).

∴ Sets A and B are equal.