# DefinitionsEdit

## SubsetEdit

Subset means for all x, if x is in A then x is also in B.

## Proper SubsetEdit

## UnionEdit

## IntersectionEdit

## Empty SetEdit

## MinusEdit

## PowersetEdit

## Ordered PairEdit

## Cartesian ProductEdit

or

## RelationEdit

A set of ordered pairs

### DomainEdit

### RangeEdit

### FieldEdit

## Equivalence RelationsEdit

**Reflexive:**A binary relation R on A is reflexive iff for all a in A, <a, a> in R**Symmetric:**A rel R is symmetric iff for all a, b if <a, b> in R then <b, a> R**Transitive:**A relation R is transitive iff for all a, b, and c if <a, b> in R and <b, c> in R then <a, c> in R

## Partial OrderingEdit

- Transitive and,
**Irreflexive:**for all a, <a, a> not in R

### TrichotomyEdit

Exactly **one** of the following holds

- x < y
- x = y
- y < x