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

Comments

Post a Comment

Popular posts from this blog

ML Aggarwal Solution Class 10 Chapter 15 Circles Exercise 15.1

Image
 Exercise 15.1 Question 1 Using the given information, find the value of x in each of the following figures : Sol : (i) ∠ADB and ∠ACB are in the same segment. ∠ADB = ∠ACB = 50° Now in ∆ADB, ∠DAB + X + ∠ADB = 180° (Angles of a triangles) $\Rightarrow 42^{\circ}+x+50^{\circ}=180^{\circ}$ $\Rightarrow x+92^{\circ}=180^{\circ}$ $\Rightarrow x=180^{\circ}-92^{\circ}=88^{\circ}$ (ii) ∠ABD=∠ACD (Angles in the same segment) But ∠ACD=32° ∴∠ABD=32° Now in ΔABD ∠ABD+∠ADB+∠DAB=180° ⇒32°+45°+x=180° ⇒77°+x=180° ⇒x=180°-77°=103° (iii) ∠BAD=∠BCD (Angles in the same segement) But ∠BAD=20° $\therefore \angle B C D=20^{\circ}$ $\because \angle \mathrm{CEA}=90^{\circ}$ $\therefore \angle \mathrm{CED}=90^{\circ}$ Now in $\Delta$ CED, $\angle C E D+\angle B C D+\angle C D E=180^{\circ}$ $\Rightarrow 90^{\circ}+20^{\circ}+x=180^{\circ}$ $\Rightarrow 110^{\circ}+x=180^{\circ}$ $\Rightarrow x=180^{\circ}-110^{\circ}=70^{\circ}$ (iv) In ΔABC ∠ABC+∠ACB+∠BAC=180° (∵Sum of angles of a triangle) $\Rightarrow 69...
Read more

ML Aggarwal Solution Class 9 Chapter 20 Statistics Exercise 20.2

  Exercise 20.2 Question 1 Sol : (i) discrete  (ii) continuous  (iii) discrete  (iv) continuous  (v) continuous  Question 2 Sol : Given data  13, 6, 10 ,5 ,11 ,14 ,2 ,8 ,15 ,16 ,9 ,13 ,17 ,11, 19 ,5 ,7 ,12 ,20 ,21 ,18 ,1 ,8 ,12 ,18 Classes 0-4 5-9 10-14 15-9 20-24 Frequency 2 7 8 6 2 Question 3 Sol : (i)  Classes 1-10 11-20 21-30 31-40 Frequency 8 7 6 6 (ii) Range = Maximum value - Minimum value  =40-2=38 (iii) Third class of frequency table $=\frac{21+30}{2}=\frac{51}{2}$ =25.5 Question 4 Sol : Variate : A particular value of a variable is called variate Class size :  The difference be...
Read more

ML Aggarwal Solution Class 9 Chapter 3 Expansions Exercise 3.2

Exercise 3.2 Question 1 Sol : Given : x-y=8..(i) xy=5...(ii) Squaring both sides in equation (i) ∴(x-y) 2 =8 2 ⇒x 2 -2.xy+y 2 =64 ⇒x 2 -2(5)+y 2 =64 ⇒x 2 +y 2 =64+10 ⇒x 2 +y 2 =74 Question 2 Sol : ⇒Given : x+y=10...(i) ⇒xy=21....(ii) Squaring both sides in equation (i) ⇒(x+y) 2 =10 2 ⇒x 2 +2xy+y 2 =100 ⇒x 2 +2(21)+y 2 =100 ⇒x 2 +4 2 +y 2 =100 ⇒x 2 +y 2 =100-42 ⇒x 2 +y 2 =58 2(x 2 +y 2 )=2×58=116 Question 3 Sol : ⇒Given : 2a+3b=7..(i) ⇒ab=2....(ii) Squaring both sides in equal (i) ⇒(2a+3b) 2 =7 2 ⇒(2a) 2 +2.2a+3b+(3b) 2 =49 ⇒4a 2 +12ab+9b 2 =49 ⇒4a 2 +12(2)+9b 2 =49 ⇒4a 2 +24+9b 2 =49 ⇒4a 2 +9b 2 =49-24 ⇒4a 2 +9b 2 =25 Question 4 Sol : ⇒Given : 3x-4y=16...(i) ⇒xy=4..(ii) Squaring on both sides in equation (i) ⇒(3x-4y) 2 =16 2 ⇒(3x) 2 -2.3x.4y+(4y) 2 =256 ⇒9x 2 -24xy+16y 2 =256 ⇒9x 2 -24(4)+16y 2 =256 ⇒9x 2 -96+16y 2 =256 ⇒9x 2 +16y 2 =256+96 ⇒9x 2 +16y 2 =352 Question 5 Sol : ⇒Given : x+y=8...(i) ⇒x-y=2...(ii) Since we know that ⇒2(x) 2 +2(y) 2 =(x+y) 2 +(x-y) 2 From (i) ⇒S...
Read more