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NDA 2023 Maths · Mathematics · Sets, Relations and Functions · medium

If n(A)=20, n(B)=15 and n(A∩ B)=5, then the number of elements belonging to exactly one of the sets A and B is

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If n(A)=20n(A)=20, n(B)=15n(B)=15 and n(A∩B)=5n(A\cap B)=5, then the number of elements belonging to exactly one of the sets AA and BB is
  1. A. 2020
  2. B. 2525
  3. C. 3030
  4. D. 3535
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Answer: (B) 2525

Elements only in AA: 20−5=1520-5=15; only in BB: 15−5=1015-5=10. So exactly one set contains 2525 elements. Equivalently n(A∪B)−n(A∩B)=30−5=25n(A\cup B)-n(A\cap B)=30-5=25. The value 3030 is n(A∪B)n(A\cup B), which also counts the common elements.
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