If a set A contains 3 elements and another set B contains 6 elements, then what is the minimum number of elements that (A∪B) can have?

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NDA (Held On: 17 Nov 2019) Maths Previous Year paper
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  1. 3
  2. 6
  3. 8
  4. 9

Answer (Detailed Solution Below)

Option 2 : 6
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Concept:

If A and B are two sets then, n (A ∪ B) = n (A) + n (B) - n (A ∩ B)

Calculation:

Given: n (A) = 3 and n (B) = 6.

As we know that, if A and B are two sets then, n (A ∪ B) = n (A) + n (B) - n (A ∩ B)

⇒ n (A ∪ B) = 3 + 6 - n (A ∩ B)

In order to minimize n (A ∪ B) we have to maximize n (A ∩ B) .

If A is a subset of B, then A ∩ B = A ⇒ n (A ∩ B) = n (A) = 3

⇒ n (A ∪ B) = 3 + 6 - 3 = 6.

Hence, the minimum number of elements that (A∪B) can have is 6.
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