Set Theory Formulas & Identities

Set theory Formulas

We are going to share Set Theory Formulas for the student who is studying in the class of 5, 6, 7, 8, 9, 10, 11, and 12. In math, set theory is a very important topic which is helping to improve scores in the exam. If you want to become very intelligent in math then you should remember the Set theory Formulas to resolve set theory related problems. If you have any questions related to the set theory please let me know through the comment and mail. There are millions of students looking for set theory formulas that why we shared set theory formulas below.

Set Theory Identities

  • Sets: A, B, C
  • Universal Set: I
  • Complement: A’
  • Proper Subset: A ⊂ B
  • Empty Set: ∅
  • Union of Sets: A ∪ B
  • Intersection of Sets: A ∩ B
  • Difference of Set: A\B

Set Theory Formulas

  • A⊂I
  • A⊂A
  • A=B if A⊂B and B⊂A
  • Empty Set: ∅⊂A
  • Union of Sets: C = A∪B = {X|X∈A or X∈B}
  • Union of Commutative Sets: A∪B = B∪A
  • Union of Associativity Sets: A∪(B∪C) = (A∪B)∪C
  • Intersection of Sets: C = A∩B = {X|X∈A or X∈B}
  • Intersection of Commutative Sets: A∩B = B∩A
  • Intersection of Associativity Sets: A∩(B∩C) = (A∩B)∩C
  • Distributive: A∪(B∩C) = (A∪B)∩(A∪C) and A∩(B∪C) = (A∩B)∪(A∩C)
  • Idempotency: A∪A = A, A∪A = A
  • Domination: A∩∅ = ∅, A∪I = I
  • Identity: A∪∅ = A, A∩I = A
  • Complement = A’= {X∈I|X∉A}
  • Complement of intersection and Union: A∪A’ = I, A∩A’ = ∅
  • De Morgan’s Law: (A∪B)’ = A’∩B’, (A∩B)’ = A’∪B’
  • Difference Sets: C = B\A = {X|X∈B or X∉A}
  • B\A = B\(A∩B)
  • B\A = B∩A’
  • A\A = ∅
  • A\B = A if A∩B = ∅
  • (A\B)∩C=(A∩C)\(B∩C)
  • A’ = I\A
  • Cartesian Product : C = A X B = {(x,y)| X∈A and y∈B}

Download Set Theory Formula in PDF

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