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

Question

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

Smart Achievers · Accepted Answer

(3)

$∵$ $U = {x : x^{5} - 6 x^{4} + 11 x^{3} - 6 x^{2} = 0} = {0, 1, 2, 3}$

$A = {x : x^{2} - 5 x + 6 = 0} = {2, 3}$

$and$ $B = {x : x^{2} - 3 x + 2 = 0} = {1, 2}$

$∴$ $A \cap B = {2}$

$Hence, (A \cap B)' = U - (A \cap B) = {0, 1, 2, 3} - {2} = {0, 1, 3}$

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