The sum of all the elements in the set $\{n \in \{1, 2, \ldots, 100\} \mid \text{H.C.F. of } n \text{ and } 2040 \text{ is } 1\}$ is equal to $.....$

If $U$ is the universal set with $100$ elements; $A$ and $B$ are two sets such that $n(A)=50$,$n(B)=60$,and $n(A \cap B)=20$,then find $n(A^{\prime} \cap B^{\prime})$.

If $n(A) = 3$,$n(B) = 6$ and $A \subseteq B$. Then the number of elements in $A \cup B$ is equal to

In a city of $10,000$ families,$40\%$ families buy newspaper $A$,$20\%$ buy newspaper $B$,$10\%$ buy newspaper $C$,$5\%$ buy newspapers $A$ and $B$,$3\%$ buy $B$ and $C$,and $4\%$ buy $A$ and $C$. If $2\%$ families buy all three newspapers,find the number of families that buy only newspaper $A$.

In a group of students,$100$ students know Hindi,$50$ know English,and $25$ know both. Each student knows either Hindi or English. How many students are there in the group?

If $A$ and $B$ are two sets such that $n(A) = 70$,$n(B) = 60$,and $n(A \cup B) = 110$,then $n(A \cap B)$ is equal to: