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?

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 $n(A^{\prime} \cap B^{\prime})$.

In a city,$25\%$ of families have a telephone and $15\%$ have a car,while $65\%$ of families have neither a telephone nor a car. If $2000$ families have both a car and a telephone,then consider the following statements:
$1.$ $10\%$ of families have both a car and a telephone.
$2.$ $35\%$ of families have either a car or a telephone.
$3.$ $40,000$ families live in the city.
Which of these statements are true?

Out of all the patients in a hospital $89\%$ are found to be suffering from heart ailment and $98\%$ are suffering from lungs infection. If $K\%$ of them are suffering from both ailments,then $K$ cannot belong to the set :

$20$ 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

In a class of $300$ students,every student reads $5$ newspapers and every newspaper is read by $60$ students. Then the number of newspapers is