Relations
Subsets of A×B describing how elements relate.
Key idea
Subsets of A×B describing how elements relate.
In depth
A relation from A to B is a subset of A × B, describing which pairs are related. It can be drawn as arrows or a matrix. Properties include reflexive, symmetric, antisymmetric and transitive.
Worked example
On {1, 2, 3}, "less than" contains (1, 2), (1, 3), (2, 3).
Real-world uses
- Modelling friendships on a social network or which courses are prerequisites for others
Common mistake
Confusing a relation with a function; relations can map one input to many outputs.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Relations?
Subsets of A×B describing how elements relate. It is a topic at the advanced level in Discrete Math & Number Theory.
Where is Relations used in real life?
Real-world examples: Modelling friendships on a social network or which courses are prerequisites for others.
What should I learn before Relations?
Make sure you are comfortable with Cartesian Products, the previous topic in Discrete Math & Number Theory.
What is a common mistake with Relations?
Confusing a relation with a function; relations can map one input to many outputs.
How can I practise Relations?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Relations?
Move on to Equivalence Relations next.
Related advanced topics in Discrete Math & Number Theory
- Tautologies and Contradictions – Always true or always false statements.
- Logical Equivalence – Statements with identical truth tables.
- De Morgan’s Laws – Negation swaps AND and OR.
- Converse and Contrapositive – A conditional equals its contrapositive.
- Quantifiers – “For all” and “there exists”.
- Negating Quantified Statements – Flip the quantifier and negate the predicate.