Types Of Relations

Concept:
A relation on a set with elements is any subset of .

Total ordered pairs in .
Total number of relations .

A relation is reflexive if every element is related to itself.
That means all diagonal pairs must be present: So these pairs are fixed and cannot be chosen freely.

The remaining pairs: can either be included or excluded independently.

Step 1: Fix the reflexive pairs.
Reflexivity forces inclusion of all diagonal pairs.

Step 2: Count remaining free pairs.

Each of these pairs has 2 choices (include or exclude).