Howard Eves has a nice example in Great Moments in Mathematics (After 1650), Lecture 36: a set $K$ of elements and a relation $R$, with the following 4 postulates:

1. If $a \ne b$, then either $aRb$ or $bRa$.
2. If $aRb$, then $a \ne b$.
3. If $aRb$ and $bRc$, then $aRc$.
4. $K$ consists of exactly four distinct elements.

He then proves seven specific theorems (with more in the exercise list), and also discusses changes if some postulates are altered; then provides applications of the theorems in a variety of fields (arithmetic, geometry, and genealogy).

Howard Eves has a nice example in Great Moments in Mathematics (After 1650), Lecture 36: a set $K$ of elements and a relation $R$, with the following 4 postulates:

1. If $a \ne b$, then either $aRb$ or $bRa$.
2. If $aRb$, then $a \ne b$.
3. If $aRb$ and $bRc$, then $aRc$.
4. $K$ consists of exactly four distinct elements.

He then proves seven specific theorems (with more in the exercise list), and also discusses changes if some postulates are altered. Then he provides applications of those theorems in a variety of fields (arithmetic, geometry, and genealogy).

Howard Eves has a nice example in Great Moments in Mathematics (After 1650), Lecture 36: a set $K$ of elements and a relation $R$, with the following 4 postulates:

1. If $a \ne b$, then either $aRb$ or $bRa$.
2. If $aRb$, then $a \ne b$.
3. If $aRb$ and $bRc$, then $aRc$.
4. $K$ consists of exactly four distinct elements.

He then proves seven specific theorems (with more in the exercise list), and also discusses changes if some postulates are changes; then provides applications of the theorems in a variety of fields (arithmetic, geometry, and genealogy).

Howard Eves has a nice example in Great Moments in Mathematics (After 1650), Lecture 36: a set $K$ of elements and a relation $R$, with the following 4 postulates:

1. If $a \ne b$, then either $aRb$ or $bRa$.
2. If $aRb$, then $a \ne b$.
3. If $aRb$ and $bRc$, then $aRc$.
4. $K$ consists of exactly four distinct elements.

He then proves seven specific theorems (with more in the exercise list), and also discusses changes if some postulates are altered; then provides applications of the theorems in a variety of fields (arithmetic, geometry, and genealogy).