Set theory

Venn Diagrams

{ } φ

ξ

State whether each one is a Set or not:

(i)A collection of all people in India……………..

(ii) A collection of all fair complexioned people of India ………………………….

(iii) A collection of all good story books in our library………………..

(iv) A collection of all tall boys in our class…………..….

(v) A collection of all boys who got above 80% in Mathematics in the Annual Examination……………….

A Set

Not a Set

Not a Set

Not a Set

A Set

State whether the following sets are finite or infinite:

(i) Set of natural numbers………………….…………..…….

(ii) Set of all integers………….………………………...……..

(iii) Set of all days of the week………………………..……..

(iv) Set of all the students of our class ……………………

(v) {c: c Z , c ≤ 2 } …………………………….…………….

(vi) { y: y ≤ 4 , y N }………………………………….………….

(vii) { d: d W , d ≤ -2 }………………………………..…………

(viii) { x: x is a multiple of 4 , x Z}……………..…………

(ix) { y: y is a factor of 14, y N } …………........………….

(x) { h : h is a multiple of 5 , h Z , -10 ≤ h ≤ 10}……….

infinite

finite

infinite

finite

finite

finite

finite

finite

infinite

infinite

Express in the Roster form:

(i) set of natural numbers less than 3 =………………….

(ii) set of whole numbers less than 0 =……………………

(iii) { x : x ≤ 6 , x N } =……………………………….

(iv) { h : h = 2p , p W , p < 4 } =…………………..

1, 1, 1, 1,

2 2,2, 2,

3, 3,

3,

4,

4,

5,

5,6

{ {} } φ

0,{ }

6 8

Express in the Roster form:

(i) Set of all consonants of the word “ ANGLE”

(ii) Set of all letters of the word “ASSESS”

(iii) Set of all vowels of the word “ GEOMETRY”

(iv) Set of all planets of the Universe starting with the letter

“M”

………………..

………………..

………………..

………………..

{ }

}

}

{

{

{mercury, mars}

N,

G

L

A,

S

S

E

S

S,

G,

E,

O

M

T

R

Y

Express in the Roster form:

(i) { b: b N , 1 < b < 7 } = ….…………………..

(ii) { c: c = 3n , n W , n ≤ 5 } = …..…………….

(iii) { y : y N , 3 ≤ y < 7 } = ……………………

(iv) { x : x is a factor of 24 } = ……………………….

(v){ z : z is a composite number,12 < z < 20}=……………….

{2, 3 , 4 , 5 , 6 }

{ 0, 3, 6, 9, 12, 15 }

{ 3, 4, 5, 6 }

{ 1, 2, 3 , 4, 6 , 8, 12 }

{14, 15, 16, 18}

Express in the Set Builder Form:

(i) { a, e, i, o, u } =……………….……………………….

(ii) { January, June, July } = ….…………………..…..

(iii) { 0, 1, 2, 3, 4, 5, 6} =…………….…………………..

(iv) { 2 , 4 , 6, 8, 10 , 12, 14 } =……………..…………….

(v) { -2 , -1, 0, 1 } =……………….……………………….

{x: x is a set of all vowels}

{ x: x is the name of a month starting with the letter “J”}

{x : x W , x < 7 }

{ x : x = 2n, n N ,n ≤ 7}

{ x : x Z , -3 < x < 2 }

State true or false:

(i) {x : x W , x < 1} is an empty set …..………………

(ii) { x : x N , 34 < x < 35 } is an empty set……......

(iii) { φ } is an empty set …………………………………….

(iv) { 0 } is a NULL set…………………………………………

(v) φ = { } ………………………………………………………….

(vi) { x : x = 2n , x W , n < 3 } = { 2 , 4 } ………………

(vii) { x: x N , x < 1 } = { }……….……….……………….

(viii) { x: x is a factor of 18 } = { 2 ,3 ,6 , 9} ……………

(ix) { y: y is a factor of 15 } = {1, 3, 5, 15}……………...

(x) {a , b , e} and {1, 2, 3} are equivalent sets…….….

False

True

False

False

False

False

True

True

True

True

If A = { a,b,c,d,e,f} B = { a,c,d,f,g,h}

Find :

A B =……………….

A B =…….....................................

{

{ }

}a,

b,

c,

d,

e,

f

a,

b,

c,

d,

f,

e,

g, g,

h h,

A B

The shaded portion is ……………..(Click to get the answer)

A B

P Q

The shaded portion is ……………..(Click to get the answer)

P Q

A

B

(i) Which portion is A B = …………….

(ii) Which portion is A B = …………….

B

A

P

Q

What is P Q = ………………….. Φ(Null Set)

6

What is :

(i) A B =

3

8

12

4

11

7

5

910

ξ

1

2A B

(ii) B =

{ 3,8,12}

{5,6,10}

{1,2}

{4,7,9,11}

{3,5,6,7,8,9,10,11,12}

{5,6,8,10}

Choose the correct option:

A

a

bc

d

e

What is H P = ………………….

What is H P = ………………….

H

P

{a, b}

{a, b, c, d, e}

X

Y

Z

1

2 3

4

5 67

8

9

10

(i) X Y = ………………..............

(ii) X Y = ...……………...........…

(iii) Y Z =……..……............….…

(iv) Y Z = ……………………….….

(v) X Z = ………………

(vi) X Z = ……………….

{ 1,2, 3 ,10}

{1,2,3,4,5,6,7,8,9,10}

{ 3, 10 }

{ 1,2,3,6,7,8,10}

{3, 6,7,8, 10}

X