Count of Binary Operations on Set/Examples
Examples of Use of Count of Binary Operations on Set
Order $2$ Structure
The Cayley tables for the complete set of magmas of order $2$ are listed below.
The underlying set in all cases is $\set {a, b}$.
- $\begin{array}{r|rr}
& a & b \\
\hline a & a & a \\ b & a & a \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & a & a \\ b & a & b \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & a & a \\ b & b & a \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & a & a \\ b & b & b \\ \end{array}$
- $\begin{array}{r|rr}
& a & b \\
\hline a & a & b \\ b & a & a \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & a & b \\ b & a & b \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & a & b \\ b & b & a \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & a & b \\ b & b & b \\ \end{array}$
- $\begin{array}{r|rr}
& a & b \\
\hline a & b & a \\ b & a & a \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & b & a \\ b & a & b \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & b & a \\ b & b & a \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & b & a \\ b & b & b \\ \end{array}$
- $\begin{array}{r|rr}
& a & b \\
\hline a & b & b \\ b & a & a \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & b & b \\ b & a & b \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & b & b \\ b & b & a \\ \end{array} \qquad \begin{array}{r|rr}
& a & b \\
\hline a & b & b \\ b & b & b \\ \end{array}$