If n(A) = 73, n(B) = 69, and n(A △ B) = 88, what is n(A ∩ B)?
Answer and explanation
Correct answer: 27
For two finite sets, the number of elements in their symmetric difference is n(A △ B) = n(A) + n(B) − 2n(A ∩ B). Let n(A ∩ B) = x. Substituting the given values gives 88 = 73 + 69 − 2x = 142 − 2x. Hence, 2x = 54 and x = 27. Therefore, the intersection contains 27 elements, making option A correct.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
For two finite sets, the number of elements in their symmetric difference is n(A △ B) = n(A) + n(B) − 2n(A ∩ B). Let n(A ∩ B) = x. Substituting the given values gives 88 = 73 + 69 − 2x = 142 − 2x. Hence, 2x = 54 and x = 27. Therefore, the intersection contains 27 elements, making option A correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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