This Power point presentation is prepared to make the concepts of set more easy. Hope you will be helpful for improving your concepts.

1. SET
By: Syed Hasnain Javed Zaidi

2. SET
• Introduction to Set
• Types & Symbols of Number Sets
• Forms of Set (Descriptive, Tabular & Set Builder Notation)
• Types of Set

3. Types of Numbers

4. Symbol of Number Sets
• Natural Numbers N
• Whole Numbers W
• Set of Integers Z
• Set of Negative Integers Z-
• Set of Prime Numbers P
• Set of Even Numbers E
• Set of Odd Numbers O
• Set of Rational Numbers Q
• Set of Irrational Numbers Q’
• Set of Real Numbers R

5. • Descriptive Form
• Tabular Form
• Set Builder Notation
Forms of Set

6. • Example:
{Name of Days in a week } Descriptive Form
(Monday, Tuesday, Wednesday, Thursday, Friday, Saturday,
Sunday}
Tabular Form
{x | x is Names of days in a week} Set Builder Notation

7. • Example:
{Names of Provinces of Pakistan }
Tabular Form
{Sindh, Punjab, KPK, Balochistan}
Set Builder Notation
{x | x is a Province of Pakistan}

8. • Example:
{Set of Natural numbers less than 10 }
Tabular Form
{1, 2, 3, 4, 5, 6, 7, 8, 9}
Set Builder Notation
{x | x€N ˄ x ˂ 10}

9. • Example:
{Set of Whole numbers less than equal to 7 }
Tabular Form
{0, 1, 2, 3, 4,5, 6, 7}
Set Builder Notation
{x | x€W ˄ x ≤ 7}

10. • Example:
{Set of Integers between -100 and 100}
Tabular Form
{-99,-98,-97, ………99}
Set Builder Notation
{x | x ε Z ˄ -100 ˂ x ˂ 100}

11. Write the following in Set Builder form
i) {1, 2, 3, 4,………..100}
{x | x ε N ˄ x ≤ 100}
ii) {0, ±1, ± 2, ± 3, ± 4, ……….. ± 1000}
{x | x ε Z ˄ x ≤ 1000}
iii) { -100, -101, -102, ……….., -500}
{x | x ε Z- ˄ -100 ≤ x ≤ -500}
iv) {January, June July}
{x | x is month start from letter j}

12. v) {0, 1, 2, 3, 4,………..100}
{x | x ε W˄ x ≤ 100}
vi) { -1, - 2, - 3, - 4, ……….. - 500}
{x | x ε Z- ˄ x ≤ -500}
vii) { 100, 101, 102, ……….., 400}
{x | x ε N ˄ 100 ≤ x ≤ 400}
viii) {Peshawar, Lahore, Karachi, Quetta}
{x | x is big cities of Pakistan}

13. Write in Tabular Form
i) {x | x ε N ˄ x ≤10}
{1, 2 , 3, 4, 5, 6, 7, 8, 9, 10}
ii) {x | x ε N ˄ 4 ˂ x ˂12}
{5, 6, 7, 8, 9, 10, 11}
iii) {x | x ε W ˄ x ≤ 4}
{0, 1, 2, 3, 4}
iv) {x | x ε O ˄ 3 ˂ x ˂12}
{5, 7, 9, 11}
v) {x | x ε Z ˄ x + 1 = 0}
{-1}

14. TYPES OF SET
• Empty or Null Set
• Finite Set
• Infinite Set
• Equal Set
• Equivalent Set
• Subset
• Proper Subset
• Improper Subset
• Power Set

15. • Empty Set or Null Set:
Example:
(a) The set of whole numbers less than 0.
(b) A bald student in class 9A
(c) Let A = {x : x ∈ N 2 < x < 3}
(d) Let B = {x : x ∈ Z -1 < x < 0}
Empty or Null Set is denoted by { } or Ø
{Ø} or { 0 } is wrong

16. • Finite Set
• A set which contains a definite (countable) number of elements is called a
finite set. Empty set is also called a finite set.
For example:
• The set of all colors in the rainbow.
• N = {x : x ∈ N, x < 7}
• P = {2, 3, 5, 7, 11, 13, 17, ...... 97}
• Infinite Set
The set whose elements can not be listed (uncountable).
For Example:
• Stars in the sky
• A = {x : x ∈ N, x > 1}
• {0, -1, -2, -3, -4, ………….}

18. • Equivalent Sets:
• Two sets A and B are said to be equivalent if their cardinal number is same, i.e.,
n(A) = n(B). The symbol for denoting an equivalent set is ‘↔’.
For example:
• A = {1, 2, 3} Here n(A) = 3
• B = {p, q, r} Here n(B) = 3
Therefore, A ↔ B
• Equal sets:
• Two sets A and B are said to be equal if they contain the same elements. Every
element of A is an element of B and every element of B is an element of A.
For example:
• A = {p, q, r, s}
B = {p, s, r, q}
Therefore, A = B

19. Subset OR Proper Subset
What is Subset??
https://www.youtube.com/watch?v=_9Wvu-
R04go&list=PLmdFyQYShrjfi7EeDyHxr0jhoPXE
OlFX0&index=15
Difference b/w Subset & Proper Subset???
https://www.youtube.com/watch?v=xotLg-
oLboY

20. Subset & Proper Subsets
Q1. If A = {a, c} Final all possible subsets
{ }, {a}, {c}, {a, c}
Q2. If B = {x, y} Find Proper Subsets
{ }, {x}, {y}

21. • Power Set:
• The collection of all subsets of set A is called the power set of A. It is
denoted by P(A). In P(A), every element is a set.
For example;
• If A = {p, q} then all the subsets of A will be
P(A) = ∅, {p}, {q}, {p, q}
Number of elements of P(A) = n[P(A)] = 4 = 2n
In general, n[P(A)] = 2n where n is the number of elements in set A.