Hey Developer’s, I’m back with a new topic which is Cardinality, Set Complement and Set Laws in the series of statistics foundations.

Quick Referesher

The symbol ∈ indicates set membership and means “is an element of” so that the statement x∈A means that x is an element of the set A.

So, let’s get started …

Cardinality and Set Complement

Set Cardinality = Number of elements in a set

Ex: If A = {a,b,c}, #A = 3

Set Complement = Set of elements not contained in A (but contained elsewhere)

Ex: Die Roll : If A = {1,2,5}, then assuming S = {1,2,3,4,5,6}, Ac or A’ = S-A = {3,4,6}

Some Set Laws

De Morgan’s Laws

  • (A ⋃ B)’ = A’ ⋂ B’
  • (A ⋂ B)’ = A’ ⋃ B’

Commutative laws:

  • A ∪ B  =  B ∪ A
  • A ∩ B  =  B ∩ A

Associative laws:

  • (A ∪ B ) ∪ C  =  A ∪ (B ∪ C )
  • (A ∩ B ) ∩ C  =  A ∩ (B ∩ C )

Distributive laws:

  • A ∪ (B ∩ C )  =  (A ∪ B ) ∩ (A ∪ C )
  • A ∩ (B ∪ C )  =  (A ∩ B ) ∪ (A ∩ C )

For every two sets A and B,

  • A ∩ B and A ∩ B’ are disjoint, means do not overlap
  • A = (A ∩ B) ∪ (A ∩ B’)

Next Post will be on Experiments, Events, Sample Spaces & Points

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