$205$ students take an examination,of whom $105$ pass in English,$70$ students pass in Mathematics,and $30$ students pass in both. How many students fail in both subjects?

If $X$ and $Y$ are two sets such that $X \cup Y$ has $50$ elements,$X$ has $28$ elements and $Y$ has $32$ elements,how many elements does $X \cap Y$ have?

The number of elements in the set $\{ n \in \mathbb{N} : 10 \leq n \leq 100 \text{ and } 3^n - 3 \text{ is a multiple of } 7 \}$ is $........$.

Let $X$ be the set consisting of the first $2018$ terms of the arithmetic progression $1, 6, 11, \dots$ and $Y$ be the set consisting of the first $2018$ terms of the arithmetic progression $9, 16, 23, \dots$. Then,the number of elements in the set $X \cup Y$ is:

$20$ teachers of a school either teach mathematics or physics. $12$ of them teach mathematics while $4$ teach both the subjects. Then the number of teachers teaching physics is

If $A = \{1, 2, 3, 4, 5, 6\}$,then the number of subsets of $A$ which contain at least two elements is