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Question

Given U={x:xN,x9}, A={x:x is divisible by 2} and B={x:x3N}, where U is the universal set. Then, (AB)(AB) = ____. (3 mark)

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Solution

U={x:xN,x9}

U={1, 2, 3, 4, 5, 6, 7, 8, 9}

A={x:x is divisible by 2}

A={2, 4, 6, 8}

B={x:x3N}

B={3, 6, 9} (1 mark)

AB is the set of elements belonging to A or B.

AB={2, 3, 4, 6, 8, 9}

AB is the set of elements belonging to both A and B.

AB={6} (1 mark)

(AB)(AB) is the set of elements belonging to only AB, and not (AB).

(AB)(AB)={2, 3, 4, 6, 8, 9}{6}

={2,3,4,8,9} (1 mark)


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