First slide

Operations on Sets

Question

Universal set $U = \{x : x^{5} - 6 x^{4} + 11 x^{3} - 6 x^{2} = 0\}$ , $A = \{x : x^{2} - 5 x + 6 = 0\}$ and $B = \{x : x^{2} - 3 x + 2 = 0\}$ then the number of elements in $(A \cap B)^{'}$ is equal to

Moderate

Solution

$\begin{matrix} U = \{x : x^{5} - 6 x^{4} + 11 x^{3} - 6 x^{2} = 0\} = {0, 1, 2, 3} \\ A = \{x : x^{2} - 5 x + 6 = 0\} = {2, 3} \\ and B = \{x : x^{2} - 3 x + 2 = 0\} = {2, 1} \\ ∴ (A \cap B)^{'} = U - (A \cap B) \\ = {0, 1, 2, 3} - {2} = {0, 1, 3} \end{matrix}$

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