Previous Year NEET Question- Set Theory

• 2018: Let $A, B$ be finite sets. If $n(A) = 10$ and $n(A \cup B) = 15$, then the maximum possible value of $n(B)$ is 15.

This is because the cardinality of the union of two sets is always greater than or equal to the cardinality of either set. In this case, $n(A) = 10$ and $n(A \cup B) = 15$, so $n(B) \leq 15$. However, $n(B)$ cannot be less than $n(A \cup B) - n(A) = 15 - 10 = 5$. Therefore, the maximum possible value of $n(B)$ is 15.

• 2017: Let $A$ be a set of $n$ distinct elements. Then the number of ways of selecting two subsets $A_1$ and $A_2$ of $A$ such that $A_1 \cap A_2 = \phi$ and $A_1 \cup A_2 =