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

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maximum value of $n (A \cup B) = 21$

minimum value of $n (A \cap B) = 0$

maximum value of $n (A \cap B) = 3$

minimum value of $n (A \cup B) = 7$

answer is C.

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Detailed Solution

Let $n (A) = α, n (B) = β, (α > β)$

Given $2^{α} - 2^{β} = 120 \Rightarrow α = 7, β = 3$

$∴ n (A \cup B) \in [7, 10]$

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