# CSCE 222 Lecture 10

Jump to navigation
Jump to search

« previous | *Friday, February 11, 2011* | next »

## Truth Sets

Let be a predicate with domain .

The set of all elements x in D such that P(x) is true is denoted by:

### Set operations

Let be a universal set.

Let , then

## Fun with Sets

(Oh boy!)

Suppose that and are finite sets.

How many elements are in their union?

## Big O — Redefined

Big O is actually a set of all functions asymptotically less than a given function (read as a subset of O(n)) What is the set ?

## Functions

Let and be nonempty sets. A function that maps from to is an assignment of exactly one element of to each element of .

:

- is domain (input type)
- is codomain (output type; superset of range)
- is range

### Example

### Injective Functions

Function is one-to-one (A maps uniquely to B)

### Surjective Functions

Range of A is B