(see if and only if)

(see negation, universal qlantifier)

(see Set Equality)

The cardinality of a set is the number of elements in a finite set, denoted with magnitude or absolute value bars, denoted as or

(see Set Builder Notation)

If is a finite set with cardinality , then . This is why the power set is sometimes denoted as .

(see If and Only If)

(see if and only if)

For the relation

For the relation

For two relations and :

Domain properties:

Range properties (nearly identical):

Pretty self evident

For , , :

1. Assosiative:
2. Inverse distributive:
3. Domain identity:
4. Range identity:
5. Identity: ,

For and :

For , :

For :

1. Idempotent:
2. Associative: