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NTA Abhyas JEE Main2020MathematicsSets and RelationsPractice

If the difference between the number of subsets of the sets A and B is 120 , then choose the incorrect option.

Options

  1. AMaximum value of n A ∩ B = 3
  2. BMinimum value of n A ∩ B = 0
  3. CMaximum value of n A ∪ B = 21
  4. DMinimum value of n A ∪ B = 7

Correct answer

C. Maximum value of n A ∪ B = 21

Step-by-step solution

Let, n A = α , n B = β α > β given, 2 α - 2 β = 120 ⇒ α = 7 , β = 3 ∴ n A ∩ B ∈ 0 , 3 ∵ n A ∪ B = α + β = n A ∩ B n A ∪ B ∈ 7 , 10

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