Intersection and Union

The intersection of two sets A and B is the set of elements common to both A and B. The symbol is "$\cap$"

$\text{A}\cap \text{B}$

The union of two sets A and B is the set of elements in A or B (or both). The symbol is "$\cup$"

$\text{A}\cup \text{B}$

Complement Set

Given a set A, the complement of A is the set off all elements in the universal set U, but not in A. We can write ${\text{A}}^{\text{c}}$

Properties of Set Operation

A. Commutative

$\text{A}\cap \text{B}=\text{B}\cap \text{A}$ $\text{A}\cup \text{B}=\text{B}\cup \text{A}$

B. Distributive

$\text{A}\cup (\text{B}\cap \text{C})=(\text{A}\cup \text{B})\cap (\text{A}\cup \text{C})$

$\text{A}\cap (\text{B}\cup \text{C})=(\text{A}\cap \text{B})\cup (\text{A}\cap \text{C})$

C. De'Morgan Theorem

$(\text{A}\cup \text{B}{)}^{\text{c}}={\text{A}}^{\text{c}}\cap {\text{B}}^{\text{c}}$ $(\text{A}\cap \text{B}{)}^{\text{c}}={\text{A}}^{\text{c}}\cup {\text{B}}^{\text{c}}$