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 probabilities that a student passes in Mathematics,Physics,and Chemistry are $m, p$,and $c$ respectively. The student has a $75\%$ chance of passing in at least one,a $50\%$ chance of passing in at least two,and a $40\%$ chance of passing in exactly two. Which of the following relations are true?

In a committee,$50$ people speak French,$20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of these two languages?

Two newspapers $A$ and $B$ are published in a city. It is known that $25\%$ of the city population reads $A$ and $20\%$ reads $B$,while $8\%$ reads both $A$ and $B$. Further,$30\%$ of those who read $A$ but not $B$ look into advertisements,$40\%$ of those who read $B$ but not $A$ look into advertisements,and $50\%$ of those who read both $A$ and $B$ look into advertisements. The percentage of the population who look into advertisements is:

If $P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28, P(ABC) = 0.09, P(A \cup B \cup C) \ge 0.75$ and $P(BC) = x$,then find the range of $x$.

In a survey of $60$ people,it was found that $25$ people read newspaper $H$,$26$ read newspaper $T$,$26$ read newspaper $I$,$9$ read both $H$ and $I$,$11$ read both $H$ and $T$,$8$ read both $T$ and $I$,and $3$ read all three newspapers. Find the number of people who read exactly one newspaper.