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Set and Notations Mathematics, Cheat Sheet of Mathematics

Mathematics

Simple set and notations mathematics

Typology: Cheat Sheet

2025/2026

Uploaded on 03/21/2026

wang-zhaojun
wang-zhaojun 🇸🇬

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Topic 1SetLanguages and Notations 5ᵗʰJanuary2026
11Sets
collectionof objects whichare clearlyidentified
A12,3 4,5
eetment eachelementisunique
aDefining aSet
iDescribingtheelements
words Ais aset of positiveodd
numberslessthan 8
setbuildernotations AIngpositiveodd
number
Ciil Listing the elements A1,35,7
12Symbols in setnotationlanguage
can is an elementof eg
2.3
bis not an elementof eg 2.3
ccis asubset of eg PEQ everyelementof
P12,33 Pis also an
element of Q
dcis apropersubsetof Q1,23,4 DQu
eg Pc Qeveryelementof
Pis also an PQ
element of Q
eis not asubsetof eg PQPabc
Q12,33
note for subsets sequencesdoesNot matter
pf3
pf4
pf5

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Download Set and Notations Mathematics and more Cheat Sheet Mathematics in PDF only on Docsity!

Topic

Set

Languages

and

Notations

January

1 Sets

collection

of

objects which are

clearly

identified

A

1

2,

eetment

each

element is unique

a

Defining

a

Set

i Describingtheelements

words

A

is a set of

positive

odd

numbersless

than 8

set

builder

notations

A

Ing

positive

odd

number

Ciil

Listing

the elements A

Symbols

in setnotation language

can

is an

element of

eg

b

is

not

an element of eg

c c

is

a subset of eg

PEQ

every

elementof

P

1 2,

Pis

also

an

element of Q

d c is a proper

subset

of

Q

D

Qu

eg Pc

Q

every element

of

P

is also

an P Q

element of Q

e is not a subset of

eg

P

Q

P a

b c

Q

1

note for

subsets

sequences

does Not matter

f

U

union

g

n

s intersection

h

null set

empty

set

does

not contain

any element

nothing

is here eg

A

odd

numbers divisible by

2

A

or

A 3

3 Representing number of elements in

a set

h

A represents

the

number ofelements in set A

eg

F XE

n

F 7

F

2

3, 5,6 7,

there are 7 elements

50 F is a finite set

eg

G x x is aneven

number

n

G

a

50 F is a

infinite

set

1

Equal

Sets

same number

of elements

elements are

identical

order

is

NOT

important

eg

A

u

B

in in

A B

remember

A x x

3 73

A

B as x 16

can

be

B

x x 16

on 42

1 7 Intersection of sets

Common

element

to both sets

eg

A 1

B

1,4 73

thus

A

n B

A

intersect

B

I is the element

of the

set An B

Union of Sets

Combine

elements

from

bothsets

eg

A 1

B

1,4 73

thus

AU

B

1

2 3 4, A

union B

1

9 Complement

of a set

set of

elements which

are not members

of

a

knownset

eg

Known

set

A

members of

Universal set

E

Unknown set

A

prime

if

EE but X

A

then

EAI

OA

shaded

Venn Diagrams