If |A| = 28, |B| = 35, and |A ∪ B| = 50, what is |A \ B|?
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Answer and explanation
Correct answer: 15
Use the cardinality formula |A ∪ B| = |A| + |B| − |A ∩ B|. Thus, 50 = 28 + 35 − |A ∩ B|, so |A ∩ B| = 13. The set difference A \ B contains the elements that are in A but not in B, so |A \ B| = |A| − |A ∩ B| = 28 − 13 = 15. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
Use the cardinality formula |A ∪ B| = |A| + |B| − |A ∩ B|. Thus, 50 = 28 + 35 − |A ∩ B|, so |A ∩ B| = 13. The set difference A \ B contains the elements that are in A but not in B, so |A \ B| = |A| − |A ∩ B| = 28 − 13 = 15. Therefore, 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).
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