If |A| = 41, |B| = 36, and |A \ B| = 19, what is |A ∪ B|?
Answer and explanation
Correct answer: 55
The set A \ B contains elements of A that are not in B. Since |A| = 41 and |A \ B| = 19, the elements common to A and B number |A ∩ B| = 41 − 19 = 22. Apply the inclusion–exclusion formula: |A ∪ B| = |A| + |B| − |A ∩ B|. Hence |A ∪ B| = 41 + 36 − 22 = 55. Subtracting the intersection prevents the common elements from being counted twice.
Frequently asked questions
What is the correct answer to this question?
55
Why is this the correct answer?
The set A \ B contains elements of A that are not in B. Since |A| = 41 and |A \ B| = 19, the elements common to A and B number |A ∩ B| = 41 − 19 = 22. Apply the inclusion–exclusion formula: |A ∪ B| = |A| + |B| − |A ∩ B|. Hence |A ∪ B| = 41 + 36 − 22 = 55. Subtracting the intersection prevents the common elements from being counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
