# All Sets Formulas List

## Venn Diagrams for 2 Sets

#### Venn Diagram Formula for 2 sets / circles: Where,
A only = A - (A∩B)
B only = B - (A∩B)

## Venn Diagrams for 3 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)

## 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

## A Union B

#### Formula: 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

## A Intersect B

#### Formula: 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

## Set Difference

#### Formula: 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.

## Symmetric Difference

#### Formula: 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.

## 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

## Distributive Property

#### Formula:

a(b + c) = ab + ac