If set A contains 15 elements, set B contains 10 elements, and the intersection of A and B contains 5 elements, how many elements are in the union of sets A and B?
Practice Questions
1 question
Q1
If set A contains 15 elements, set B contains 10 elements, and the intersection of A and B contains 5 elements, how many elements are in the union of sets A and B?
20
25
10
15
The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 15 + 10 - 5 = 20.
Questions & Step-by-step Solutions
1 item
Q
Q: If set A contains 15 elements, set B contains 10 elements, and the intersection of A and B contains 5 elements, how many elements are in the union of sets A and B?
Solution: The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 15 + 10 - 5 = 20.
Steps: 7
Step 1: Identify the number of elements in set A. Set A has 15 elements.
Step 2: Identify the number of elements in set B. Set B has 10 elements.
Step 3: Identify the number of elements in the intersection of sets A and B. The intersection (common elements) 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| = 15 + 10 - 5.
Step 6: Calculate the result: 15 + 10 = 25, then 25 - 5 = 20.
Step 7: Conclude that the number of elements in the union of sets A and B is 20.
