Set Theory

Symbols

Number Sets​
Natural​
Whole​
Integers​
Rational​
Irrational (Complement of )​
Real ()​
Empty Set​

Set Operations and Properties

  • Sets have no order
  • No duplicates

Subsets

  • Def. means all elements in are contained in

A set is always a subset of itself.

Unions

  • Def. Combine all elements of two sets (or operation)
Example

Let


  • Ex.
  • Ex.
  • Ex. we cannot be more simple than this

Intersections

  • Def. A set with all elements common to two sets (and operation)
Example

Let


  • Ex.
  • Ex.

Empty Set

  • Def. The empty set is a set which exists but contains nothing

  • Ex.

  • Ex.

  • Ex.

The empty set is always a subset.