University Discrete Math Sets, Functions and Relations — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 13 definitions and 4 theorems, 8 worked examples, 2 diagrams, in 16 printable pages. This page lists what the notes cover. The notes themselves come with the University Discrete Math bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Sets, Functions and Relations — what the notes cover
9 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Set notation, subsets and power sets
- Definition — Sets and the two notations
- Definition — Subsets and power sets
Also in this section: 1 worked example, 1 note on method and common errors.
Set operations and Venn diagrams
- Definition — The set operations
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Proving set identities
- Theorem — The laws of set algebra
- Definition — Three ways to prove a set identity
Also in this section: 1 worked example, 1 note on method and common errors.
Injective, surjective and bijective functions
- Definition — Functions, domain, codomain and image
- Definition — Injective, surjective and bijective
- Theorem — Injections, surjections and the size of a finite set
Also in this section: 1 worked example, 1 note on method and common errors.
Composition and inverse functions
- Definition — Composition and the identity function
- Theorem — When a function has an inverse
Also in this section: 1 worked example, 1 note on method and common errors.
Relations and their properties
- Definition — Relation on a set
- Definition — The four properties
Also in this section: 1 worked example, 1 note on method and common errors.
Equivalence relations and partitions
- Definition — Equivalence relation and equivalence classes
- Theorem — Classes and partitions
Also in this section: 1 worked example, 1 note on method and common errors.
Partial orders and Hasse diagrams
- Definition — Partial order
- Definition — Hasse diagram
- Definition — Minimal, maximal, least and greatest
Also in this section: 1 worked example, 1 diagram.
Where the notes are
The notes are one of the documents in the University Discrete Math Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Sets, Functions and Relations practice worksheet is free and stays free.
Every University Discrete Math topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Discrete Math units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Sets, Functions and Relations practice worksheet About the Sets, Functions and Relations unit test