List of All Sets Formulas

All Sets Formulas List

Venn Diagrams for 2 Sets

Venn Diagram Formula for 2 sets / circles:

Venn Diagrams for Two Sets


Where,
A only = A - (A∩B)
B only = B - (A∩B)

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Venn Diagrams for 3 Sets


Venn Diagrams for Three Sets


Where,

A only = A - ( ab + x + ca ),

B only = B - ( bc + x + ab ),

C only = C - ( bc + x + ca ),

AB = (AnB) - x,

BC = (BnC) - x,

CA = (Cna) - x,

x = AnBnC,

D = U - (A only + B only + C only + AB + BC + CA + x)


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Subset of Set

Formula:

For a set B to be a subset of A,
Each and every element in the set B should be present in the set A

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A Union B

Formula:

Union of Two Sets
A∪B = {a1,a2,a3,a4,...,an} with ai∈A or ai∈B,i=1,2,3,...n


Where,

A and B represents the set A and set B

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A Intersect B

Formula:

Intersection of Two Sets
A∩B = {a1,a2,a3,a4,...,an} with ai∈A and ai∈B,i=1,2,3...n

Where,

A and B represents the set A and set B

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Set Difference

Formula:

Universal set
U \ A = {a1,a2,a3,..an} ai∈U and ai∉A,i=1,2,3...n

Where,

U represents the Universal set,
A represents the set A.

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Symmetric Difference

Formula:

Symmetric Difference
A Δ B = {a1,a2,a3,..an} ai∈A and ai∉B,i=1,2,3...n

Where,

A represents the set A,
B represents the set B.

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Complement of Sets

Formula:


A- or A' or Ac = U - A


Where,

A = Set A
U = Universal Set
A- or A' or Ac = Complement of Set A

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Distributive Property

Formula:

a(b + c) = ab + ac

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