This document defines mathematical concepts related to sets including: 1. Types of sets such as finite, infinite, empty sets. 2. Set operations including union, intersection, complement, difference. 3. Notations for representing sets in tubular and set builder forms. 4. Relationships between sets such as equal sets, equivalent sets, and the power set of a set. 5. Common sets of numbers such as natural numbers, integers, rational numbers.

1. , , , ,
, ,
5
5, 10, 15, 20, 25, 30, 35, ...
X2
- 4 = 0 2, -2
1. ,
2. A, B, C, ...
3.
1. A 1 5
A
2. B
B
Empty Set) { } (phi)
1 2
Finite Set)
0
{1, 2, 3, ...,100} 100
Infinite Set)
{1, 2, 3, ...}
1 A, 2 A, 3 A, 4 A, 5 A
-----------------------------------------------
0 A, 6 A
a B, e B, i B, o B, u
----------------------------------------------
b B, c B
1 2 3
4 5
a e i
o u

2. A B A
B
A B A B
A B A B
A = {1, 2} B = {2, 3}
C = {1, 2, 3} D = {1, 2, 3, 4}
A B, A C, A D
B A, B C, B D
C A, C B, C D
D A, D B, D C
1. A A)
2. A)
3. A A =
4. A B B C A C
5. A = B A B B A
A
5
A
1, 2, 3, 4
B
2x - 1)(x + 4) = 0
B
-4

3. 4
1. Union) A B A B
A B
2.
Intersection)
A B
A B
A B
3.
Complement)
A
A
A'
4.
Difference)
A B
A
B
A - B
= {1, 2, 3, ..., 20}, A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8, 10, 12}
A B = {1, 2, 3, 4, 5, 6, 8, 10, 12} A B = {2, 4, 6}
A' = {7, 8, 9, ..., 20} B' = {1, 3, 5, 7, 9, 11, ...,20}
(A B)' = {7, 9, 11, 13, ..., 20} (A B)' = {1, 3, 5, 7, ..., 20}
A - B = {1, 3, 5} B - A = {8, 10, 12}
2
1) Tubular form)

4. 1.
2. ,)
3.
4. 3 3
Tripple dot)
2) Set builder form)
1.
2. | (|
{x | x}
A
5
A = {1, 2, 3, 4}
A = {x | x
5}
B
B = { ,
,
, ,
,
, }
B = {x | x
}
C C = {a, b, c, ... ,z}
C = {y | y
}
1. Equal Sets)
A B A = B
A B A B
A = {1, 2, 3, 4, 5}
B = {1, 2, 3, 4, 3, 2, 5,
5, 5}
A B A = B
C = {a, e, i, o, u}
D = {i, o, u, e, o}
C D C = D
E = {0, 1, 3, 5}
F = {x | x I+
, x < 6}
E 4 0, 1, 3, 5 F 5
1, 2, 3, 4, 5
E F
G = { , ,
} G H G H

5. H = { , ,
}
2.
Equivalentl Sets)
A B A B
A = {a, b, c, d, e}
B = {1, 2, 3, 4, 5}
A B
1:1
A B
C = {x | x I+
}
D = {x | x = 2n , n =
1, 2, 3, ...}
C {1, 2, 3, ...}
D 2 {2, 4, 6, ...}
C D 1:1
C D
1. A = B A B
2. A B A = B
A A A
P(A)
A P(A)
{ }
{a} { , {a}}
{a, b} { , {a}, {b}, {a, b}}
{a, b, c} { , {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
1.

6. 2.
-
A
A B A
B
A B A
B
A B A = B
N
I+
I-
I
Q
Q'
R+
R-
R