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

Correct answer: C. Maximum value of n(A B) = 21 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]

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

If the difference between the number of subsets of the sets A and B...

If the difference between the number of subsets of the sets

A

and

B

120

, then choose the incorrect option.

Options

AMaximum value of $n\left(A \cap B\right) = 3$
BMinimum value of $n\left(A \cap B\right) = 0$
CMaximum value of $n\left(A \cup B\right) = 21$
DMinimum value of $n\left(A \cup B\right) = 7$

Correct answer

C. Maximum value of $n\left(A \cup B\right) = 21$

Step-by-step solution

Let,&

n \left(A\right) = \alpha,n \left(

B\right) =

\beta\left(\alpha

\beta\right)<br />given, {2}^{\alpha}

{2}^{\beta}

= 120 ⇒

\alpha =7, \beta =3

∴ n \left(

A \cap B\right) \in \left[0, 3\right] ∵ n\left(A \cup B\right) = \alpha + \beta = n\left(A \cap B\right)

<br />

n \left(A \cup B\right) \in \left[7, 10\right]

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