# Topic 8 – Option: Sets, relations and groups

## Sets

## Venn Diagrams

## Cartesian Product

## Relations

## Functions

## Functions

## Functions

- f(x) notation
- Domain and range
- Exam Questions - Domain and range
- Even & Odd Functions
- Combination of functions
- The inverse of a function
- Self inverse functions
- Graphical relationship between f(x) and its inverse
- Exam Questions - Inverse functions
- Exam Questions - Functions
- Injections, surjections, bijections
- Composition of functions and inverse functions

## Binary Operations

## Binary Operations

## Groups

## Groups

- What defines a group
- Different types of groups
- Commutative groups
- Order of a group
- Subgroups
- Lagrange’s theorem
- Generators
- Proof that all cyclic groups are Abelian
- Permutations under composition of permutations
- Cycle notation for permutations
- Result that every permutation can be written as a composition of disjoint cycles
- The order of a combination of cycles