Question

If $U = \{x : x^5 - 6x^4 + 11x^3 - 6x^2 = 0\}$ and
$A = \{x : x^2 - 5x + 6 = 0\}$ and $B = \{x : x^2 - 3x + 2 = 0\}$, then $(A \cap B)' =$

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

Answer 1

Answer: (C)

$\because U = \left\{x : x^{5}-6x^{4}+11x^{3}-6x^{2} = 0\right\} = \left\{0, 1, 2, 3\right\}$
$A = \left\{x : x^{2} - 5x+6 = 0\right\} = \left\{2, 3\right\}$
and $B = \left\{x : x^{2}-3x+2 = 0\right\} = \left\{1, 2\right\}$
$\therefore A \cap B = \left\{2\right\}$
Hence, $\left(A \cap B\right)' = U - \left(A \cap B\right)$
$= \left\{0, 1, 2, 3\right\} - \left\{2\right\} = \left\{0, 1, 3\right\}$