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Properties of Set Operation

Universal set...

Question

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

{1, 3}

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{1, 2, 3}

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{0, 1, 3}

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{0, 1, 2, 3}

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Solution

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

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Similar questions

U = {x | x^{5} - 6 x^{4} + 11 x^{3} - 6 x^{2} = 0}

A = {x | x^{2} - 5 x + 6 = 0}

B = {x | x^{2} - 3 x + 2 = 0}

(A \cap B)^{'}

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

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

B = {x : x^{2} - 3 x + 2 = 0}

(A \cap B)^{'}

A = {x | x is an integer root of the equation x^{5} - 6 x^{4} + 11 x^{3} - 6 x^{2} = 0}

B = {x | x is a real root of the equation a x^{5} + 2 a x^{3} + 2 b x^{2} + b = 0, a, b \in R such that the given equation have maximum number of real roots.}

P = {x / x^{2} + 14 x + 40 = 0}

Q = {x / x^{2} - 5 x + 6 = 0}

R = {x / x^{2} + 17 x - 60 = 0}

X = {- 20, - 10, - 4, 2, 3, 4}

P \cup Q

6 x^{2} - 13 x + 6 = 0

\sqrt{6} x^{2} - 5 x + \sqrt{6} = 0

24 x^{2} - 17 x + 3 = 0

x^{2} + 2 x + 4 = 0

x^{2} + x + 1 = 0

x^{2} - 3 \sqrt{3} x - 30 = 0

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