# Set Theory Symbols

**Symbol**

**Meaning / definition**

**Example**

{ }

a collection of elements

A = {3,7,9,14},

B = {9,14,28}

B = {9,14,28}

A ∩ B

objects that belong to set A and set B

A ∩ B = {9,14}

A ∪ B

objects that belong to set A or set B

A ∪ B = {3,7,9,14,28}

A ⊆ B

subset has fewer elements or equal to the set

{9,14,28} ⊆ {9,14,28}

A ⊂ B

subset has fewer elements than the set

{9,14} ⊂ {9,14,28}

A ⊄ B

left set not a subset of right set

{9,66} ⊄ {9,14,28}

A ⊇ B

set A has more elements or equal to the set B

{9,14,28} ⊇ {9,14,28}

A ⊃ B

set A has more elements than set B

{9,14,28} ⊃ {9,14}

A ⊅ B

set A is not a superset of set B

{9,14,28} ⊅ {9,66}

2

^{power set}all subsets of A

all subsets of A

A = B

both sets have the same members

A={3,9,14},

B={3,9,14},

A=B

B={3,9,14},

A=B

A

^{c}all the objects that do not belong to set A

A \ B

objects that belong to A and not to B

A = {3,9,14},

B = {1,2,3},

A-B = {9,14}

B = {1,2,3},

A-B = {9,14}

A – B

objects that belong to A and not to B

A = {3,9,14},

B = {1,2,3},

A-B = {9,14}

B = {1,2,3},

A-B = {9,14}

A ∆ B

objects that belong to A or B but not to their intersection

A = {3,9,14},

B = {1,2,3},

A ∆ B = {1,2,9,14}

B = {1,2,3},

A ∆ B = {1,2,9,14}

A ⊖ B

objects that belong to A or B but not to their intersection

A = {3,9,14},

B = {1,2,3},

A ⊖ B = {1,2,9,14}

B = {1,2,3},

A ⊖ B = {1,2,9,14}

*a*∈A

set membership

A={3,9,14}, 3 ∈ A

*x*∉A

no set membership

A={3,9,14}, 1 ∉ A

(

*a*,*b*)collection of 2 elements

A×B

set of all ordered pairs from A and B

|A|

the number of elements of set A

A={3,9,14}, |A|=3

#A

the number of elements of set A

A={3,9,14}, #A=3

infinite cardinality of natural numbers set

cardinality of countable ordinal numbers set

Ø

Ø = { }

C = {Ø}

set of all possible values

_{0}

_{0}= {0,1,2,3,4,…}

0 ∈

_{0}_{1}

_{1}= {1,2,3,4,5,…}

6 ∈

_{1} = {…-3,-2,-1,0,1,2,3,…}

-6 ∈

= {

*x*|*x*=*a*/*b*,*a*,*b*∈}2/6 ∈

= {

*x*| -∞ <*x*<∞}6.343434 ∈

= {

*z*|*z=a*+*bi*, -∞<*a*<∞, -∞<*b*<∞}6+2

*i*∈