Question

Universal set,
$U = \{x | x^5 - 6x^4 + 11x^3 - 6x^2 = 0\}$
$A = \{x | x^2 - 5x + 6 = 0\}$
$B = \{x | x^2 - 3x + 2 = 0\}$
What is $(A \cap B)'$ equal to ?

• A. {1, 3}
• B. {1, 2, 3}
• C. {0, 1, 3}
• D. {0, 1, 2, 3}

Answer 1

Answer: (C)

$U = \{x : x^5 - 6x^4 + 11x^3 - 6x^2 = 0\}$
Solving for values of x, we get
$U = \{0, 1, 2, 3\}$
$A = \{x : x^2 - 5x + 6 = 0\}$
Solving for values of x, we get
$A = \{2, 3\}$
and $B = \{x : x^2 - 3x + 2 = 0\}$
Solving for values of x, we get
$B = \{2, 1\}$
$A \cap B = \{2\}$
$ \therefore \, (A \cap B)' = U - (A \cap B)$
$= \{0, 1, 2, 3\} - \{2\} = \{0, 1, 3\}$