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NDA 2025 Maths · Mathematics · Sets, Relations and Functions · medium

If n(A)=20, n(B)=15 and n(A∩ B)=8, then the number of elements in the symmetric difference Atriangle B is

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If n(A)=20n(A)=20, n(B)=15n(B)=15 and n(A∩B)=8n(A\cap B)=8, then the number of elements in the symmetric difference A△BA\triangle B is
  1. A. 2727
  2. B. 1919
  3. C. 1212
  4. D. 3535
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Answer: (B) 1919

n(A∪B)=20+15−8=27n(A\cup B)=20+15-8=27. The symmetric difference removes the common part: n(A△B)=27−8=19n(A\triangle B)=27-8=19, equivalently (20−8)+(15−8)=12+7=19(20-8)+(15-8)=12+7=19. The value 2727 is the union, not the symmetric difference.
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