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Formulas for Set Theory

December 19, 2020

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
Formula Sets
set theory formulas

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)