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0 votes
7.2k views
in Mathematics by (57.5k points)

Universal set, 

U = {x | x5 - 6x4 + 11x3 - 6x2 = 0} 

A = {x | x2 - 5x + 6 =  0}

B = {x | x2 - 3x + 2 = 0}

What is the value of (A ∩ B)′ ? 

(a) {1, 3}              (b) {1, 2, 3} 

(c) {0, 1, 3}          (d) {0, 1, 2, 3}

1 Answer

+1 vote
by (63.7k points)
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Best answer

Correct option is (c)

Explanation:

U = {x : x5 - 6x4 + 11x3 - 6x2 = 0} = {0,1,2,3}

A = {x : x2 - 5x + 6 = 0} = {2,3}

and B = {x : x2 - 3x + 2 = 0} = {2,1}

A ∩ B = {2} 

∴ (A ∩ B)′ = U - (A ∩ B)

= {0,1,2,3} - {2} = {0,1,3}

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