If $A = \{x, y\}$,then the power set of $A$ is

$A$ class has $175$ students. The following data shows the number of students obtaining one or more subjects: Mathematics $100$,Physics $70$,Chemistry $40$; Mathematics and Physics $30$,Mathematics and Chemistry $28$,Physics and Chemistry $23$; Mathematics,Physics and Chemistry $18$. How many students have offered Mathematics alone?

Sets $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $A \cup B$?

If $A = \{1, 2, 3, 4, 5\}, B = \{2, 4, 6\}, C = \{3, 4, 6\},$ then $(A \cup B) \cap C$ is

Let $n(U) = 700, n(A) = 200, n(B) = 300$ and $n(A \cap B) = 100,$ then $n(A^c \cap B^c) = $

Given $n(U) = 20$,$n(A) = 12$,$n(B) = 9$,$n(A \cap B) = 4$,where $U$ is the universal set,$A$ and $B$ are subsets of $U$,then $n((A \cup B)^C) = $