Hey Developer’s, I’m back with a new topic which is a Sets Membership and Set Operations in the series of statistics foundations.

Quick Referesher

Set Theory : A branch of mathematics that deals with sets.

Then, what is Sets: It is a well defined collection of distinct objects.

So, let’s get started …

Set Membership

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.

Set Membership

Consider a set A = {1,2,3,4,5}

We can state that 1 is an element of A : 1 ∈ A

And that 6 is not an element of A: 6 ∉ A

This notation is often used to specify a set of values.

Example: “For all even natural numbers”: For all x: {x ∈ N | x is even }

Empty Set

It is basically a set that contains no elements : ∅ = { }

For every element x, x ∉ ∅

Subsets

It is basically the part of the large set of group. Subset is a part of large set.

Subsets

Set A is a subset of set B if every element of A is in B.

For Ex: A = {1,2,3}, B={1,2,3,4,5}, A is a subset of B: A ⊂ B

Similary, we have a “not subset of” operator, so if C = {1,6} : C ⊄ B

For every set A, ∅ ⊂ A and A ⊂ A

Set Union

A union of two sets A and B is basically a set that contains all the elements from A and B, and the common elements do not repeat.

Set Union

Ex: if A = {1,2,3} and B = {1,x,∞} then A ⋃ B = {1,2,3,x,∞}

Set Intersection

An intersection of two sets A and B is a set containing all that belong to both A and B.

Basically the common elements from both the sets.

Set Intersection

Ex: if A = {1,2,3} and B = {1,x,∞} then A ⋂ B = {1}

Set Difference

The relative complement or set difference of sets A and B denoted A – B, is the set of all elements in A that are not in B.

Set Difference

Ex: If A = {1,2,3} and B = {3,4,5} then A – B = {1,2}

Next Post will be on Cardinality, Set Complement and Set Laws

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