M L Aggarwal Solutions for Chapter: Sets, Exercise 6: CHAPTER TEST

Let $\xi =$the set of all letters in the word $\text{'}\mathrm{TAMILNADU}\text{'}$ and    

$X=\{x:x$ is a vowel and $x\in \xi \}$. What is the cardinal number of the power set of X?

If $n\left(\xi \right)=30, n\left(A\text{'}\right)=15, n\left(B\right)=5$ and $n\left(A\cap B\right)=3,$ find $n\left(A\right)$.

In a group of $50$ students, the number of students studying French, English and Sanskrit were found to be as follows :

French$=17$, English$=13$, Sanskrit$=15$;

French and English  $=9$, English and Sanskrit $=4$, French and Sanskrit $=5$

English, French and Sanskrit $=3$.

Find the number of students who study English only.

In a group of $50$ students, the number of students studying French, English and Sanskrit were found to be as follows :

French$=17$, English$=13$, Sanskrit$=15$;

French and English  $=9$, English and Sanskrit $=4$, French and Sanskrit $=5$

English, French and Sanskrit $=3$.

Find the number of students who study: French and English but not Sanskrit

In a group of $50$ students, the number of students studying French, English and Sanskrit were found to be as follows :

French$=17$, English$=13$, Sanskrit$=15$;

French and English  $=9$, English and Sanskrit $=4$, French and Sanskrit $=5$

English, French and Sanskrit $=3$.

Find the number of students who study Sanskrit only

In a group of $50$ students, the number of students studying French, English and Sanskrit were found to be as follows :

French$=17$, English$=13$, Sanskrit$=15$;

French and English  $=9$, English and Sanskrit $=4$, French and Sanskrit $=5$

English, French and Sanskrit $=3$.

Find the number of students who study English and Sanskrit but not French.

In a group of $50$ students, the number of students studying French, English and Sanskrit were found to be as follows :

French$=17$, English$=13$, Sanskrit$=15$;

French and English  $=9$, English and Sanskrit $=4$, French and Sanskrit $=5$

English, French and Sanskrit $=3$.

Find the number of students who study at least one of the three languages.

In a group of $50$ students, the number of students studying French, English and Sanskrit were found to be as follows.

French$=17$, English$=13$, Sanskrit$=15$;

French and English  $=9$, English and Sanskrit $=4$, French and Sanskrit $=5$

English, French and Sanskrit $=3$.

Find the number of students who study none of the three languages.