# 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**R****Transitive: A relation R is transitive iff for all a, b, and c if <a, b> in R and 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

# Proof StrategiesEdit

## If, thenEdit

Prove if x then y

- Suppose x
- ...
- ...
- so, y

## If and only IfEdit

Prove x iff y

- suppose x
- ...
- ...
- so, y
- suppose y
- ...
- ...
- so, x

## EqualityEdit

Prove x = y

- show x subset y
- and
- show y subset x

## Non-EqualityEdit

Prove x != y

- x = {has p}
- y = {has p}
- a in x, but a not in y