Q. Universal set, $U = \{ x:x^{5} - 6x^{4} + 11x^{3} - 6x^{2} = 0\}$ And $A = \{ x:x^{2} - 5x + 6 = 0\}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \{ x:x^{2} - 3x + 2 = 0\}$ Then, $(A \cap B)'$ is equal to
A) {1, 3}
B) {1, 2, 3}
C) {0, 1, 3}
D) {0, 1, 2, 3}
Explanation
(c)
$U = \left\{ x:x^{5} + 6x^{4} + 11x^{3} - 6x^{2} = 0 \right\} = \left\{ 0,\ 1,\ 2,\ 3 \right\}$
$A = \left\{ x:x^{2} - 5x + 6 = 0 \right\} = \{ 2,\ 3\}$
And $B = \left\{ x:x^{2} - 3x + 2 = 0 \right\} = \{ 2,\ 1\}$
$\therefore\ \ (A \cap B)^{'} = U - (A \cap B)$
$= \left\{ 0,\ 1,\ 2,\ 3 \right\} - \left\{ 2 \right\} = \{ 0,\ 1,\ 3\}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.