If |A \ B| = 17, |B \ A| = 23, and |A ∩ B| = 14, what is |A ∪ B|?
Answer and explanation
Correct answer: 54
The union A ∪ B is divided into three mutually disjoint regions: elements that are only in A, elements that are only in B, and elements common to both sets. These regions have sizes |A \ B| = 17, |B \ A| = 23, and |A ∩ B| = 14. Since they do not overlap with one another, add them directly: |A ∪ B| = 17 + 23 + 14 = 54. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
54
Why is this the correct answer?
The union A ∪ B is divided into three mutually disjoint regions: elements that are only in A, elements that are only in B, and elements common to both sets. These regions have sizes |A \ B| = 17, |B \ A| = 23, and |A ∩ B| = 14. Since they do not overlap with one another, add them directly: |A ∪ B| = 17 + 23 + 14 = 54. Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
