Naïve Set Theory

Basic Definitions

Basic Definitions

Basic Definitions

Basic Definitions

Basic Definitions

The Empty Set

The Empty Set

The Empty Set

The Universal Subset

Warnings

Text Problems

Theorem 2.1(b)

Theorem 2.2

Proper Subsets

Power Sets

Power Sets

Power Sets

Power Sets

Text Problems

Set Operations

Venn Diagrams

Complements

Russell's Paradox

The Halting Problem

Propositions

φ ∩ A = φ

φ ∪ A = A

φ ∪ A = A (again)

A ∩ B ⊆ A

If A ⊆ B then A ∪ C ⊆ B ∪ C

Propositions

(A ∪ B)~ = A~ ∩ B~

A - B = A ∩ B~

A ⊆ B iff B~ ⊆ A~