LearnViz CompSci
Home / Learn / Theory & Discrete Math / Functions and Relations

Beginner Topic 4 of 51 Theory & Discrete Math

Functions and Relations

Mappings and pairings between sets.

How it works

A relation is a set of ordered pairs; a function maps each input to exactly one output. Properties: injective (one-to-one), surjective (onto), bijective. Relations can be reflexive, symmetric, transitive.

Where it is used

Hash functions, equivalence classes, databases.

Common pitfall

Not every relation is a function.

Where it fits in the course

Functions and Relations is topic 4 of 51 in Theory & Discrete Math, rated Beginner. It follows Sets and Set Operations. The next topic is Mathematical Induction.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Theory & Discrete Math quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Functions and Relations?
Mappings and pairings between sets. It belongs to Theory & Discrete Math and is a beginner-level topic.
Where do people use Functions and Relations?
Hash functions, equivalence classes, databases.
What is the most common mistake with Functions and Relations?
Not every relation is a function.
What should I learn before this topic?
Start with Sets and Set Operations, the topic just before it in Theory & Discrete Math.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Theory & Discrete Math quiz.
Is Functions and Relations hard to learn?
It is a Beginner topic, so it works as an entry point. If the terms are new, read the explanation twice and try the visualizer before the quiz.
How long does it take to learn Functions and Relations?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Functions and Relations?
Sets and Set Operations, Mathematical Induction, Predicate Logic are closely connected. The full list is in the related topics section of this page.
What should I study after Functions and Relations?
Continue with Mathematical Induction, the next topic in Theory & Discrete Math.

Related topics