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  4. If n( A )=10, n( A ∩ B )=4, then how many elements are in (A ∩ B) prime ∩ A

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Q. If $n( A )=10, n( A \cap B )=4$, then how many elements are in $(A \cap B)^{\prime} \cap A$

NTA AbhyasNTA Abhyas 2022

Solution:

$n( A \cap B )^{\prime} \cap A =n A ^{\prime} \cup B ^{\prime} \cap A$
$=n A ^{\prime} \cap A \cup B ^{\prime} \cap A$
$=n B ^{\prime} \cap A$
$=n( A )-n( A \cap B )$
$\Rightarrow n( A \cap B )^{\prime} \cap A =10-4=6$