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}, A^{c} 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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