ML AGGARWAL CLASS 8 CHAPTER 6 Operation on Sets Venn Diagrams Exercise 6.2

Exercise 6.2

Question 1

Sol :

(i) A={0,5,7,8,9,11}

(ii) B={2,5,6,8}

(iii) $\xi=\{0,1,2,4,5,6,7,8,9,11,12\}$

(iv) $A^{\prime}=\{1,2,4,12\}$

(v) $B^{\prime}=\{0,1,4,7,9,11,12\}$

(vi) $A \cup B=\{0,2,5,6,7,8,9,11\}$

(vii) $A \cap B=\{5,8\}$

(viii) $(A \cup B)^{\prime}=\{1,4,12\}$

(ix) $(A \cap B)^{\prime}=\{0,1,2,4,6,7,9,11, 12\}$

Question 2

Sol :

(i) P={a, b, d, f, g, h, i}

(ii) Q={b, d, e}

(iii) $\xi=\{a, b, c, d, e, f, q, h, i\}$

(iv) $p^{\prime}=\{c, j\}$

(v) $Q^{\prime}=\{a, c, f, g, h, i, j\}$

(vii) $p \cap Q=\{b, d, e\}$

(viii) $(p \cup Q)^{\prime}=\{c, j\}$

(ix) $(P \cap Q)^{\prime}=\{a, C, f, g, h, 1, j\}$

Question 3

Sol :

(i) $\xi=\{0,1,2,3,4,5,6,7,8,9,10,11,12\}$

(ii) $A \cap B=\{0,5,8\}$

(iii) $A \cap B \cap C=\{0,5\}$

(iv) $C^{\prime}=\{2,7,8,9,10,11,12\}$

(v) $A-C=A \cap C^{\prime}=\{8,10\}$

(vi) $B-C=B \cap C^{\prime}=\{7,8,11\}$

(vii) $C-B=C \cap B^{\prime}=\{3,4,6\}$

(viii) $(A \cup B)^{\prime}=\{2,4,6,9,12)$

(ix) $(A \cup B \cup C)^{\prime}=\{2,9,12\}$

Question 4

Sol :

(i) $\begin{aligned} A &=\{x \mid x \in N, x=2 n, n \leq 5\} ; B=\{x \mid x \in W, x=4 n, n<5\} \\ A &=\{2,4,6,8,10\} \quad B=\{4,8,12,16\} \end{aligned}$

(ii) $\begin{aligned} A=\{\text { prime factors of } 42) & B=\{\text { prime factors of } 60\} \\ A=\{2,3,7\} & B=\{2,3,5\} \end{aligned}$

(iii) $\begin{aligned} P=\{x \mid x \in W, x<10\} \quad Q &\{\text { prime factor of } 210\} \\ & P=\{0,1,2,3,4,5,6,7,8,9\} \quad Q,\{2,3,7,5\} \end{aligned}$

Question 5

Sol :

$n(A)=22 \quad n(B)=18 \quad n(A \cap B)=5$

(i) $n(A \cup B)=17+5+13=35$

(ii) $n(A-B)=n(A)-n(A \cap B)=17-5=12$

(iii) $n(B-A)=\eta(B)-n(A \cap B)=13-5=8$

Question 6

Sol :

$n(A)=25 \quad n(B)=16, n(A \cap B)=6, n\left((A \cup B)^{\prime}\right)=5$

(i) $n(A \cup B)=19+6+10=35$

(ii) $n(\xi)=n(A \cup B)+n\left((A \cup B)^{\prime}\right)=35+5=40$

(iii) $n(A-B)=\eta(A)-n(A \cap B)=25-6=19$

(iv) $n(B-A)=n(B)-n(A \cap B)=16-6=10$

Question 7

Sol :

$n(\xi)=25 \quad n\left(A^{\prime}\right)=7 \quad n(B)=10 \quad B C A$

$n(A)=n(\xi)-n\left(A^{\prime}\right)=25-7=18$

$n(A-B)=n(A)-n(A \cap B)=18-10=8$

$\therefore$ Cardinal number of set A-B is 8

Question 8

Sol :

(i) No of boys who play at least one of the two games

$\begin{array}{l}=20+12+5 \\=37\end{array}$

(ii) Neither cricket nor fast ball 

$\begin{aligned} n\left((A \cup B)^{\prime}\right) &=\text { Total student }-n(A \cup B) \\ &=50-37=13 \end{aligned}$

Question 9

Sol :

(i) Both Orange and Banana.

$n(A \cap B)$ = no of students who like both orange and banana 

                        =no of student who like orange - no of students who like orange but not banana

= 32- 26

= 6 

(ii) $\begin{aligned} n(B)=& ? \\ n(A \cup B)-n(A)+n(B)-n &(A \cap B) \\ n(B)=40-32+6=& 46-32 \\=& 14 \end{aligned}$

number of student who like only banana =14-6=8

Question 10

Sol :

$n(A \cap B)=x$

$n(A \cup B)=n(A)+n(B)-n(A \cap B)$

60=45+28-x

x=73-60

x=13

∴ no of people who speak both Bengali and English are 13