EXERCISE 1.6

If $X$ and $Y$ are two sets such that $n\left(X\right)=17, n\left(Y\right)=23$ and $n\left(X\cup Y\right)=38,$ find $n\left(X\cap Y\right).$

If $X$ and $Y$ are two sets such that $X\cup Y$ has $18$ elements, $X$ has $8$ elements and $Y$ has $15$ elements; how many elements does $X\cap Y$ have?

In a group of $400$ people, $250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?

If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements and $S\cap T$ has $11$ elements, how many elements does $S\cup T$ have?

If $X$ and $Y$ are two sets such that $X$ has $40$ elements, $X\cup Y$ has $60$ elements and $X\cap Y$ has $10$ elements, how many elements does $Y$ have?

In a group of $70$ people, $37$ like coffee, $52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

In a group of $65$ people, $40$ like cricket, $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

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?