ML AGGARWAL CLASS 8 CHAPTER 6 Operation on Sets Venn Diagrams Excercise 6.1

Exercise 6.1

Question 1

Sol :
A={0,1,2,3,4,5,6,7,8}    B={3,5,7,9,11},   C={0,5,10,20}

(i) AB={0,1,2,3,4,5,6,7,8,9,11}

(ii) AC={0,1,2,3,4,5,6,7,8,10,20}

(iii) BC={0,3,5,7,9,10,11,20}

(iv) AB={3,5,7}

(v) AC={0,5}

(vi) BC={5}

As B⋃C has 8 elements, n(BC)=8

As AB has 3 elements, n(AB)=3

As AC has 2 elements, n(AC)=2

As BC has 1 element, η(BC)=1


Question 2

Sol :

(i)

A={0,1,4,7} and $\xi=\{x \mid x \in w, x \leq 10\}$

Given ξ={0,1,2,3,4,5,6,7,8,9,10}

Complement of A=A={2,3,5,6,8,9,10}


(ii)

A={ Consonants } and ξ={ alphabets of English }

Complement of A=A, {vowels}

={a, e, i, o,u}


(iii) A = {boys in class viii of all schools in bengaluru} and 

ξ = {student in class viii of all school in bengaluru}

Complement of A=A, {girls in class viii of all school in bengaluru}


(iv) A={ letter of KAlKA} and ξ={ letters of KOlKATA}

Complement of A=A={0,T}


(v) A={ odd natural numbers\} and ξ={ Whole numbers\}

Complement of A=A={0,2,4,6,8,10,12.}

 

Question 3

Sol :

A={x:xN and 3<x<7} and B={x:xω and x4}

A={4,5,6} and B={0,1,2,3,4}

(i) AB={0,1,2,3,4,5,6}

(ii) AB={4}

(iii) A-B={5,6}$

in B-A=\{0,1,2,3}


Question 4

Sol :

p={0,1,2,3,4,5}Q={4,5,6,7,8}

(i) pQ={0,1,2,3,4,5,6,7,1}

(ii) PQ={4,5}

(iii) P-Q={0,1,2,3}

(iv) Q-P={6,7,8}

yes  pQ is a proper superset of  pQ but vice versa is not possible 
since A contains elements not in B.



Question 5

Sol :

A={ letters of ward INTEGRITY\} B={ letters of word  ReckonING} 

(i) AB={I,N,T,E,G,R,Y,C,0}

(ii) AB={I,N,E,G,R}

(iii) A-B={T, Y}

(iv) B-A={c, k, 0}


(a) n(A)=7η(B)=8n(AB)=5n(AB)=10

n(AB)=2n(BA)=3

n(A)+n(B)n(AB):7+85=10=η(AB)


(b) η(AB)n(B)=108=2=n(AB)

η(A)n(AB)=75=2=n(AB)


(c) η(AB)n(A)=107=3=η(BA)

η(B)n(AB)=85=3=η(BA)


d) η(AB)+n(BA)+n(AB)=2+3+5=10=n(AB)



Question 6

Sol :

ξ={10,11,12,13,14 .. 40}

A={5,10,15,20,2530,35,40}

B={6,12,18,24,30,36}....(3)

(i) AB={5,6,10,12,15,18,20,24,25,30,35,40}

AB={30}

(i) η(A)=8,n(B)=6,n(AB)=1η(AB)=13

η(A)+η(B)n(AB)=8+61:13=n(AB)


Question 7

Sol :

(i) A={5,9}

(ii) B={1,2,3,5,7,9}

(iii) AB={1,2,3,4,6,7,8}

(iv) AB={4,6,8}

(v) AB=AB={1,2,3,7,}

(vi) BA=BA={3

(ii) (AB)={1,2,3,5,7,9}

(viii) AB={1,2,3,5,7,9}


(a) (AB)=AB={1,2,3,5,7,9} verified

(b) n(A)=7η(A)=2η(ξ)=9

 n(A)+n\left(A^{\prime}\right)=7+2=9=n(\xi) \text { verified }


(c)n(AB)+n((AB))

n(AB)=3;n((AB))=6

6+3=9=η(ξ). verified


(d) n(AB)=4η(BA)=0n(AB)=3

η(AB)+η(BA)+n(AB)=4+0+3=7=n(AB)



Question 8

Sol :

ξ1={x:xw,x10},A={x:x5}B={x:3x<8}

ξ={0,1,2,3,4,5,6,7,8,9,10}A={5,6,7,8,9,10}

B={3,4,5,6,7}

(i)
 AB={3,4,5,6,7,8,9,10}A={0,1,2,3,4}(AB)={0,1,2}B:{0,1,2,8;9,10}AB={0,1,2}

 ∴ (AB)=AB={0,1,2}

(ii)
 AB={5,6,7}1(AB)={0,1,2,3,4,8,9,10}
AB={0,1,2,3,4,8,9,10}

 ∴ (AB)=AUB

(iii) 
AB={8,9,10}AB={8,9,10}AB=AB

(iv) 
BA={3,4}BA={3,4}BA=BA




Question 9

Sol :

n(A)=20,n(B)=16,n(AB)=30n(AB)=?

we know n(AB)=n(A)+n(B)n(AB)

30=20+16n(AB)

n(AB)=3630=6n(AB)=C

n(AB)=c


Question 10

Sol :

n(5)=20:n(A)=7n(A)=?

We know n(A)+n(A)=n(ξ1)

n(A)=20-7=13

n(A)=13


Question 11

Sol :

n(ξ1)=40n(A)=20n(B)=16n(AB)=32

n(B)+n(B)=n(ξ)n(B)=4016=24.n(B)=24

n(AB)=D(A)+η(B)D(AB)
32=20+24n(AB)
n(AB)=4432=12
n(B)=24;n(AB)=12


Question 12

Sol :

n(ξ1)=32,n(A)=20,n(B)=16,n((AB))=4

(i) n(AB)=η(ξ)n(AB))=324=28

n(AB)=28


(ii) n(AB)=n(A)+n(B)n(AB)

20+28-28

36-28=8

n(AB)=8


(iii) n(AB)=n(A)n(AB)=208=12n(AB)=12




Question 13

Sol :

η(ξ)=40:n(A)=15,n(B)=12n((AB))=32

(i) n(A)=n(ξ)n(A)=4015=25


(ii) n(B)=n(Σ1)n(B)=4012=28


(iiin(AB)=n(ξ)n((AB))=4012=8


(iv) n(AB)=n(A)+n(B)n(AB)=25+128=29

(v) n(AB)=n(A)n(AB)=258=17

(vi) η(BA)=n(B)n(AB)=128=4



Question 14

Sol :

η(AB)=12,n(BA)=16,n(AB)=5

(i) n(A) ii n(B) iii n(AB)


(i)n(AB)=n(A)n(AB)n(A)=12+5=17


(ii) n(BA)=n(B)n(AB)η(B)=16+5=21


(iii) n(AB)=n(A)+h(B)n(AB)=17+215=385=33n(AB)=33

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