Question

Let the Universal Set be S. Let A and B are subsets of S. Set A contains 27 elements and Set B contains 91 elements. SetsA and B have 9 elements in common. If there are 28 elements that are in S but not in A nor B, how many elements are in s?

Answer 1

A and B are subsets of S.

Set A = contains 27 elements

Set B = contains 91 elements

A y B have 9 elemts in common

Now, to find the total elements in (Aor B), we use:

Total elements in (AorB) = Elements in A + Elements in B - (Elements in A&B)

Replacing the values:

Total elements in (AorB) = 27 + 91 - 9

Total elements in (AorB) = 109

To find the total elements in S:

S (total elements) = (element in AorB) + (elements not in A or B)

Replacing the values:

S (total elements) = 109 + 28

S (total elements) = 137

Hence, there are 137 elements in the universal set S.