# Formulas for Set Theory

## Formulas for set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.

• Set Theory formulas page is very useful in terms of exams ## Formulas of Set Theory

Notation used in set theory

Notations used in set theory:
n(A) –
Cardinal number of set A.

n(A) – Cardinality of set A.

$\overline{A}$ = Ac – complement of set A.

U – Universal

A ⊂ B – Set A is proper subset of subset of B.

A ⊆ B – Set A is subset of set B.

∅ – Null set.

a ∈ A – element “a” belongs to set A.

A ∪ B – union of set A and set B.
A ∩ B – intersection of set A and set B.

## Set Theory Formulas

1. If A and B are overlapping set, n(A ∪ B) = n(A) + n(B) – n(A ∩ B).
2. If A and B are disjoint set, n(A ∪ B) = n(A) + n(B).
3. n(A) = n(A ∪ B) + n(A ∩ B) – n(B).
4. n(A ∩ B) = n(A) + n(B) – n(A ∪  B).
5. n(B) = n(A ∪ B) + n(A ∩ B) – n(A).
6. n(U) = n(A) + n(B) – n(A ∩ B) + n((A ∪ B)c).
7. n((A ∪ B)c) = n(U) + n(A ∩ B) – n(A) – n(B).
8. n(A ∪ B) = n(A – B) + n(B – A) + n(A ∩ B).
9. n(A – B) = n(A ∪  B) – n(B).
10. n(A – B) = n(A) – n(A ∩ B).
11. n(Ac) = n(U)- n(A)