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If set A contains 10 elements, set B contains 15 elements, and the intersection

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Question: If set A contains 10 elements, set B contains 15 elements, and the intersection of A and B contains 5 elements, what is the number of elements in the union of sets A and B?

Options:

  1. 20
  2. 15
  3. 10
  4. 5

Correct Answer: 20

Solution: 

The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 10 + 15 - 5 = 20.

If set A contains 10 elements, set B contains 15 elements, and the intersection

Practice Questions

Q1
If set A contains 10 elements, set B contains 15 elements, and the intersection of A and B contains 5 elements, what is the number of elements in the union of sets A and B?
  1. 20
  2. 15
  3. 10
  4. 5

Questions & Step-by-Step Solutions

If set A contains 10 elements, set B contains 15 elements, and the intersection of A and B contains 5 elements, what is the number of elements in the union of sets A and B?
  • Step 1: Identify the number of elements in set A. In this case, set A has 10 elements.
  • Step 2: Identify the number of elements in set B. Here, set B has 15 elements.
  • Step 3: Identify the number of elements in the intersection of sets A and B. The intersection has 5 elements.
  • Step 4: Use the formula for the union of two sets: |A ∪ B| = |A| + |B| - |A ∩ B|.
  • Step 5: Substitute the values into the formula: |A ∪ B| = 10 + 15 - 5.
  • Step 6: Calculate the result: 10 + 15 = 25, then 25 - 5 = 20.
  • Step 7: Conclude that the number of elements in the union of sets A and B is 20.
  • Set Theory – Understanding the concepts of union, intersection, and the cardinality of sets.
  • Cardinality Calculation – Applying the formula for the union of two sets to find the total number of unique elements.
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