What Subsets Does Belong To

{ } ready a collection of elements A = {3,vii,9,xiv},
B = {nine,14,28} | such that and then that A = {x | x∈ $\mathbb{R}$ , x<0} A⋂B intersection objects that vest to set A and set B A ⋂ B = {ix,14} A⋃B union objects that belong to set A or set up B A ⋃ B = {3,seven,nine,14,28} A⊆B subset A is a subset of B. fix A is included in gear up 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} ⊂ {nine,14,28} A⊄B not subset set A is non a subset of set B {9,66} ⊄ {9,fourteen,28} A⊇B superset A is a superset of B. set A includes set B {9,fourteen,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} ⊃ {ix,fourteen} A⊅B not superset ready A is not a superset of set B {9,14,28} ⊅ {9,66} 2^A power set all subsets of A $\mathcal{P}(A)$ power prepare all subsets of A P(A) ability set all subsets of A ℙ(A) power set all subsets of A A=B equality both sets have the same members A={3,9,14},
B={3,nine,14},
A=B A^c complement all the objects that do non belong to set A A' complement all the objects that practise not vest to prepare A A\B relative complement objects that belong to A and non to B A = {3,9,14},
B = {1,2,3},
A \ B = {ix,14} A-B relative complement objects that belong to A and not to B A = {3,9,14},
B = {one,2,three},
A - B = {9,fourteen} A∆B symmetric deviation objects that belong to A or B but not to their intersection A = {3,9,xiv},
B = {1,2,3},
A ∆ B = {1,2,9,fourteen} A⊖B symmetric difference objects that vest to A or B but not to their intersection A = {3,nine,14},
B = {1,2,iii},
A ⊖ B = {i,two,nine,14} a∈A element of,
belongs to fix membership A={three,ix,14}, three ∈ A ten∉A not element of no set membership A={3,9,xiv}, one ∉ A (a,b) ordered pair collection of 2 elements A×B cartesian product set of all ordered pairs from A and B A×B = {(a,b)|a∈A , b∈B} |A| cardinality the number of elements of set A A={3,ix,fourteen}, |A|=3 #A cardinality the number of elements of set A A={iii,9,fourteen}, #A=three | vertical bar such that A={x|3<x<14} ℵ₀ aleph-null infinite cardinality of natural numbers set ℵ₁ aleph-one cardinality of countable ordinal numbers set Ø empty set Ø = {} A = Ø $\mathbb{U}$ universal set prepare of all possible values ℕ ₀ natural numbers / whole numbers set (with zero) $\mathbb{N}$ ₀ = {0,1,2,3,4,...} 0 ∈ $\mathbb{N}$ ₀ ℕ ₁ natural numbers / whole numbers set (without zero) $\mathbb{N}$ ₁ = {1,two,3,iv,5,...} six ∈ $\mathbb{N}$ _i ℤ integer numbers set $\mathbb{Z}$ = {...-iii,-2,-1,0,one,2,iii,...} -six ∈ $\mathbb{Z}$ ℚ rational numbers ready $\mathbb{Q}$ = {ten | x=a/b, a,b∈ $\mathbb{Z}$ and b≠0} ii/vi ∈ $\mathbb{Q}$ ℝ real numbers set $\mathbb{R}$ = {10 | -∞ < ten <∞} half-dozen.343434 ∈ $\mathbb{R}$ ℂ complex numbers set $\mathbb{C}$ = {z | z=a+bi, -∞<a<∞, -∞<b<∞} 6+2i ∈ $\mathbb{C}$