NDA 2020 Maths · Mathematics · Sets, Relations and Functions · medium

If n(A)=40, n(B)=35, n(C)=30, n(A∩ B)=15, n(B∩ C)=10, n(C∩ A)=12 and n(A∩ B∩ C)=5, then n(A∪ B∪ C) is

Single correct option

n(A)=40

n(B)=35

n(C)=30

n(A\cap B)=15

n(B\cap C)=10

n(C\cap A)=12

and

n(A\cap B\cap C)=5

, then

n(A\cup B\cup C)

Show answer and solution

Answer: (B) 73

Use inclusion-exclusion:

n(A\cup B\cup C)=105-(15+10+12)+5=105-37+5=73

. Forgetting to add back the triple intersection gives 68, a common slip, while 78 results from adding it twice.

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