Ch.2. Cartesian Product of Sets and Relations - Part 2

Concept Review


2.2 Relation

Let A and B be two sets. Then a relation R from A to B is a subset of A×B.

R is a relation from A to B => R is a subset of A×B.

Total number of relations: If A and B are two non empty sets with m and n elements respectively, A×B consists of mn ordered pairs.
Since each subset defines a relation from A to B, so total number of relations from A to B is 2^mn.


2.3 Types of relations


Void relation
Universal relation
Identity relation
Reflexive relation
Symmetric relation
Transitive relation
Antisymmetric relation
Equivalence relation


2.4 (2.5 in the book) Composition of Relations