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Question 23
Let the Universal Set, S, have 103 elements. A and B are subsets of S. Set A contains 15
elements and Set B contains 74 elements. If Sets and have 11 elements in common, how
many elements are in neither A nor B?
Answer elements
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Ask by Young Daniel. in the United States
Mar 22,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

25 elements are in neither Set A nor Set B.

Solution

Step 1:
Determine the number of elements in the union of sets and . Use the formula for the union of two sets:
Step 2:
Substitute the given values into the formula:
Step 3:
Calculate the number of elements that are in neither nor by subtracting the number of elements in the union from the total number of elements in the universal set :
elements are in neither nor .

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The Deep Dive

To determine how many elements are in neither Set A nor Set B, we can use the principle of inclusion-exclusion.
First, we calculate the total number of elements in either Set A or Set B using the formula:
Substituting the given values:
Now, the total number of elements in the universal set is 103. Thus, the number of elements in neither nor is:
So, the answer is elements.

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