If A and B are finite sets and |A \ B| = 9, |B \ A| = 4, and |A ∩ B| = 11, what is |A ∪ B|?
Answer and explanation
Correct answer: 24
The sets A \ B, B \ A, and A ∩ B represent three mutually disjoint regions in the Venn diagram. Every element of A ∪ B belongs to exactly one of these regions. Therefore, |A ∪ B| = |A \ B| + |B \ A| + |A ∩ B| = 9 + 4 + 11 = 24. Equivalently, |A| = 9 + 11 = 20 and |B| = 4 + 11 = 15, so |A ∪ B| = |A| + |B| − |A ∩ B| = 20 + 15 − 11 = 24.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
The sets A \ B, B \ A, and A ∩ B represent three mutually disjoint regions in the Venn diagram. Every element of A ∪ B belongs to exactly one of these regions. Therefore, |A ∪ B| = |A \ B| + |B \ A| + |A ∩ B| = 9 + 4 + 11 = 24. Equivalently, |A| = 9 + 11 = 20 and |B| = 4 + 11 = 15, so |A ∪ B| = |A| + |B| − |A ∩ B| = 20 + 15 − 11 = 24.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
