JEE Main 2017 · Mathematics · Sets, Relations and Functions · easy

If n(A)=20, n(B)=30 and n(A∪ B)=40, then the number of elements belonging to exactly one of A and B is

Single correct option

n(A)=20

n(B)=30

and

n(A\cup B)=40

, then the number of elements belonging to exactly one of

A

and

B

Show answer and solution

Answer: (C) $30$

Using

n(A\cup B)=n(A)+n(B)-n(A\cap B)

we get

n(A\cap B)=20+30-40=10

. Elements in exactly one set are those of the symmetric difference:

n(A\Delta B)=n(A\cup B)-n(A\cap B)=40-10=30

. A common slip is to report the intersection (10) or the sum minus union incorrectly.

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