List of set symbols of set theory and probability.

Table of set theory symbolsSymbol Symbol Name Meaning / definition Example

set a collection of elementsA = {3,7,9,14},B = {9,14,28}

intersection objects that belong to setA and set B A B = {9,14}

union objects that belong to setA or set B A B = {3,7,9,14,28}

subset subset has fewer elementsor equal to the set {9,14,28} {9,14,28}proper subset /strict subset

subset has fewer elementsthan the set {9,14} {9,14,28}

not subset left set not a subset ofright set {9,66} {9,14,28}

superset set A has more elementsor equal to the set B {9,14,28} {9,14,28}proper superset /strict superset

set A has more elementsthan set B {9,14,28} {9,14}

not superset set A is not a superset ofset B {9,14,28} {9,66}A power set all subsets of A

power set all subsets of A

equality both sets have the samemembers

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

c complement all the objects that do notbelong to set A

relativecomplement

objects that belong to Aand not to B

A = {3,9,14},B = {1,2,3},A \ B = {9,14}

relativecomplement

objects that belong to Aand not to B

A = {3,9,14},B = {1,2,3},A - B = {9,14}

symmetricdifference

objects that belong to A orB but not to theirintersection

A = {3,9,14},B = {1,2,3},A B = {1,2,9,14}

objects that belong to A or A = {3 9 14}1 of 2

difference intersection A B = {1,2,9,14}

symmetricdifference

objects that belong to A orB but not to theirintersection

A = {3,9,14},B = {1,2,3},A B = {1,2,9,14}

element of set membership A={3,9,14}, 3 Anot element of no set membership A={3,9,14}, 1 Aordered pair collection of 2 elements

cartesian product set of all ordered pairsfrom A and B

cardinality the number of elements ofset A A={3,9,14}, |A|=3

cardinality the number of elements ofset A A={3,9,14}, #A=3

aleph-null infinite cardinality ofnatural numbers set

aleph-one cardinality of countableordinal numbers set

empty set = { } C = {}

universal set set of all possible values

0natural numbers /whole numbers set (with zero)

0 = {0,1,2,3,4,...} 0 0

1natural numbers /whole numbers set (without zero)

1 = {1,2,3,4,5,...} 6 1

integer numbersset

={...-3,-2,-1,0,1,2,3,...}

-6 rational numbersset = {x | x=a/b, a,b } 2/6 real numbers set = {x | - < x