Question

What are the basic symbols in sets along with their meanings

Answer 1

Answer:

Symbol Symbol Name Meaning /

definition Example

{ } set a collection of elements A = {3,7,9,14},

B = {9,14,28}

| such that so that A = {x | x∈\mathbb{R}, x<0}

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

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

A⊆B subset A is a subset of B. set A is included in set B. {9,14,28} ⊆ {9,14,28}

A⊂B proper subset / strict subset A is a subset of B, but A is not equal to B. {9,14} ⊂ {9,14,28}

A⊄B not subset set A is not a subset of set B {9,66} ⊄ {9,14,28}

A⊇B superset A is a superset of B. set A includes set B {9,14,28} ⊇ {9,14,28}

A⊃B proper superset / strict superset A is a superset of B, but B is not equal to A. {9,14,28} ⊃ {9,14}

A⊅B not superset set A is not a superset of set B {9,14,28} ⊅ {9,66}

2A power set all subsets of A  

\mathcal{P}(A) power set all subsets of A  

A=B equality both sets have the same members A={3,9,14},

B={3,9,14},

A=B

Ac complement all the objects that do not belong to set A  

A' complement all the objects that do not belong to set A  

A\B relative complement objects that belong to A and not to B A = {3,9,14},

B = {1,2,3},

A \ B = {9,14}

A-B relative complement objects that belong to A and not to B A = {3,9,14},

B = {1,2,3},

A - B = {9,14}

A∆B symmetric difference 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}

A⊖B symmetric difference 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}

a∈A element of,

belongs to set membership A={3,9,14}, 3 ∈ A

x∉A not element of no set membership A={3,9,14}, 1 ∉ A

(a,b) ordered pair collection of 2 elements  

A×B cartesian product set of all ordered pairs from A and B  

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

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

symbol aleph-null infinite cardinality of natural numbers set  

symbol aleph-one cardinality of countable ordinal numbers set  

Ø empty set Ø = {} A = Ø