Set Theory The Language of Mathematics

{ a, v, n }

{ l, e, a, r, n }

Venn Diagram

What is Set Theory?

Set theory is a branch of mathematical logic that studies sets, which are collections of objects.

Basic Terminology

Key Terms: Set, Element, Subset, Union, Intersection.

Set Notation

Examples of set notation:

Roster Form: {a, b, c}

Set-builder Form: {x | x > 0}

1.

2.

Types of Sets

Empty Set ∅

Equal Set {1, 2, 3} = {2, 3, 1}

Singleton Set { a }

1.

5.

2.

Finite set { 1, 2, ..., 100 }

Infinite Set { 1, 2, 3, ... }

3.

4.

Equivalent Set n(A) = n(B)

Subset (⊆)

6.

7.

Proper subset (⊂) :

Superset (⊇)

Power set P(A)

Universal set U

9.

8.

10.

11.

Types of Sets conti...

Common Operations:

Set Operations

Union (A ∪ B)

Intersection (A ∩ B)

Complement (A')

Difference (A - B)

1.

2.

3.

4.

1

2

3

4

Set theory is used in linguistics, economics, and biology.

Applications of  Set Theory

Computer science

Statistics

Artificial Intelligence

Fun Fact

The concept of infinity in set theory was developed by  Georg Cantor!

Did you know

Wikipedia

Conclusion

Explore the World of Sets!

Set theory is foundational for many areas of mathematics and science!