Question

Let S be the universal set, where:

Answer 1

your answer is {0}.

Explanation:

first calculate (A intersect C) that is (0) .

then calculate {0} intersect B'compliment {3,5,6,12,14,17,18,19,20}

so your answer is {0}.

Answer 2

0

Explanation:

For the defined sets S, A, B, C, you want the size of set A∩C∩B'.

Intersection

The intersection of two sets is the set of elements contained in both. The intersection of sets A and C is the set {8}.

Complement

The complement of a set is the set of elements in the universal set that are not in the set being complemented. The complement of set B is ...

B' = {3, 5, 6, 12, 14, 17, 18, 19, 20}

A∩C∩B'

The set of elements common to AC and B' is the empty set: { }. The only element in AC is not found in B'.

The number of elements in A∩C∩B' is zero (0).

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Additional comment

In the attached, we have identified elements of set S that are in A, B, C with a 1 in the corresponding column. The intersection is found by multiplying the rows: the product is only 1 if the element is in both sets.