Set part 1

1. Set Defination, Examples, Number System Sets

2. Symbols used in SET Theory

3. Set Representations : Roaster Form and Set Builder Form

4. Types of Sets: Empty Set, Finite and Infinite Set, Equal Sets

5. Subset and its Venn Diagram Representation

6. Intervals as Subset of Real Number Set

7. Universal Set (U)

Learning Objectives

Set Defination, Examples, Number System Sets

A set is a well-defined collection of objects.

Objects, elements or members of a set are Not Repeated in that Set.

Sets are usually denoted by capital letters A, B, C, X, Y, Z, etc.

Some Examples of Sets :

Set of prime numbers less than 10 = A = { 2,3,5,7,9 }

Set of Vowels = B = { a, e, i, o, u }

These are not examples of SETs
Set of names of Good Cricketers,

Set of names of Best Indian Musicians

Set of different types of Numbers:

N, W, Z, Q, T, R, Z+, Q+, R+, Z-, Q-, R-

Some Important Symbols in Set Theory

Symbol

Symbol Name

Meaning

{ }

set

a collection of elements

Ø

empty set

Ø = { }

a ∈ Belement of OR belongs to

set membership

x ∉ Anot element of OR Not belons to

no set membership

| OR :Such that OR which satisfies

{ set of 2n | n ∈ N }

A ⊆ Bsubset

subset has few or all elements equal to the set

A ⊂ Bproper subset / strict subset

subset has fewer elements than the set

A ⊄ Bnot subset

left set is not a subset of right set

A ⊇ Bsuperset

set A has more elements or equal to the set B

A ⊃ Bproper superset / strict superset

set A has more elements than set B

A ⊅ Bnot superset

set X is not a superset of set Y

A ∪ Bunion

Elements that belong to set A or set B

A ∩ B

intersection

Elements that belong to both the sets, A and B

A-B

relative complement OR Subtraction objects that belong to A and not to B

AcOR A’ complement

all the objects that do not belong to set A

Some Important Symbols in Set Theory

Symbol

Symbol Name

Meaning

A = B

equality

both sets have the same members

P (C)

power set

all subsets of C

(a, b)

ordered pair

collection of 2 elements

A × B

cartesian product

set of all ordered pairs from A and B

|B| or n(B) cardinality

the number of elements of set B

∀

For all

∃

There Exists

∄

There Does not Exists

Iff

If and Only If

⇒

Which implies

R OR |R

real numbers set

R= {x | -∞ < x <∞}

<

Less Than

≤

Less Than or Equal to

>

Greater than

≥

Greater than or Equal to

Set Representations : Roaster Form and Set Builder Form

The set of all natural numbers which divide 42

Roaster Form or List Method

Set Builder Form or Rule Method

The set of all prime numbers and a divisor of 6

The set of all (x,y) satisfying y = x +5

Types of Sets: Empty Set, Singleton Set, Finite and Infinite Set, Equal Sets

The set of all natural numbers

The set of all prime numbers and a divisor of 6

The set of all outcomes of a Dice greater than 6
The set of all outcomes of a Dice greater than 5

A = { x : x is a letter in the word FOLLOW}

B = { y : y is a letter in the word WOLF}

Subset, Superset, Proper (strict) Subset and its Venn Diagram Representation

Set of all Real Numbers

The set of all natural numbers

The set of all prime numbers.
The set of all natural numbers

The set of all outcomes of a Dice

The set of all Even outcomes of a Dice

A = { x : x is a letter in the word FOLLOW}

B = { y : y is a letter in the word WOLF}

Intervals as Subset of Real Number Set

𝑹 =

𝑥 −∞ < 𝑥 < +∞

B =

𝑥 𝑥 ∈ 𝑹, 5 ≤ 𝑥 ≤ 10

C =

𝑥 𝑥 ∈ 𝑹, 5 ≤ 𝑥 < 10

D =

𝑥 𝑥 ∈ 𝑹, 5 < 𝑥 ≤ 10

E =

𝑥 𝑥 ∈ 𝑹, 5 < 𝑥 < 10}

Universal Set ( U )

Usually, in a particular context, we have to deal with the elements and

subsets of a Basic Set which is relevant to that particular context. For
example, while studying the system of numbers, we may interested
in the set of natural numbers N and its subsets such as the set of all

prime numbers (A) , the set of all even numbers (B), and hence N can

be Basic Set .This basic set is called the “Universal Set”. The universal
set is usually denoted by U, and all its subsets by the letters A, B etc.

𝑹 =

𝑥 −∞ < 𝑥 < +∞

𝑁 = { 1, 2, 3, … }

A =𝑥 𝑥 ∈ 𝑁, 𝑥 𝑖𝑠 𝑎 𝑝𝑟𝑖𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟

B =

𝑥 𝑥 ∈ 𝑁, 𝑥 𝑖𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 2

Note That: 𝐴 ⊂ 𝑁, 𝐵 ⊂ 𝑁, 𝑁 ⊂ 𝑅

Please Try Now..

Solve:

(a) Write the following sets in roster form:

(i) A = {x : x is an integer and –3 ≤ x < 7} (ii) E = The set of all letters in
the word TRIGONOMETRY (iii) C = {x : x ∈ N and (x – 1) (x –2) = 0}

b Write the following sets in roster form: (i) A = { 2, 4, 8, 12} (ii) B = {
1, 2, 3, 4} (iii) C = {x : x ∈ Z, – 4 < x ≤ 6}

c Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are
incorrect and why? (i) {3, 4} ⊂ A (ii) {3, 4} ∈ A (iii) {{3, 4}} ⊂ A (iv) 1 ∈ A
(v) 1 ⊂ A (vi) {1, 2, 5} ⊂ A (vii) {1, 2, 5} ∈ A (viii) {1, 2, 3} ⊂ A (ix) φ ∈ A
(x) φ ⊂ A

Try These

1. Set Defination, Examples, Number System Sets

2. Set Representations : Roaster Form and Set Builder Form

3. Types of Sets: Empty Set, Finite and Infinite Set, Equal Sets

4. Subset and its Venn Diagram Representation

5. Intervals as Subset of Real Number Set

Recap