Basic Laws Of Algebra Of Sets

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There are several laws in Statistics however, in this article, we would provide the complete list of basic fundamental laws of sets in statistics. There are seven laws of the algebra of sets and it is important to have an idea of all of them because, during calculations, they might come in handy

7 Laws Of Algebra Of Set

1. Idempotent Law

i. A ∪ A = A ii. A ∩ A = A

2. Associative Law

i. (A ∪ B) ∪ C = A ∪ (B ∪ C) ii. (A ∩ B) ∩ C = A ∩ (B∩C)

3.Commutative Law

i. A B = B ∪ A ii. A ∩ B= B ∩ A

4.Distributive Law

i. A ∪ (B∩C) = (A ∪ B) ∩ (A ∪ C)ii. A ∩ (B ∪ C) = (A ∩ B) ∪ (A∩C)

5. Identity Law

i. A ∪ ∅ = A ii. A ∩ U = A iii. A ∪ U = U iv. A ∩ ∅ = ∅

6. Complement Law

i. A ∪ A’ = U ii. A ∩ A’ = ∅ iii. (A’)’ = A iv U’ = ∅ v. ∅’ = U

7. De-morgan’s Law

i. (A ∪ B)’ = A’ ∩ B’ ii. (A ∩ B)’ = A’ ∪ B’

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