二元关系

A\times B = {(1,a),(1,b),(1,c),(2,a),(2,b),(2,c),(3,a),(3,b),(3,c),(4,a),(4,b),(4,c)}

\begin{align*} R_1 &= {(1,a),(2,a),(3,a),(4,a)}\ R_2 &= {(1,a),(2,b),(3,c)}\ R_3 &= {(2,c),(3,b),(4,a)} \end{align*}

\begin{align*} D_{R_1} &= {1,2,3,4}\ D_{R_2} &= {1,2,3}\ D_{R_3} &= {2,3,4}
\end{align*}

\begin{align*} G_{R_1} &= {a}\ G_{R_2} &= {a,b,c}\ G_{R_3} &= {a,b,c} \end{align*}

K\times K = {(j,j),(j,k),(j,l),(k,j),(k,k),(k,l),(l,j),(l,k),(l,l)}

\begin{align*} R_4 &= {(j,j),(k,k),(l,l)}\ R_5&= {(j,k),(k,l),(l,j)}\ R_6&= {(j,k),(j,l),(k,j),(k,l),(l,j),(l,k) }\ R_7 &= {(j,l),(j,k),(k,l)} \end{align*}

R_8=K\times K={(j,j),(j,k),(j,l),(k,j),(k,k),(k,l),(l,j),(l,k),(l,l)}

\Delta_{A} = {(a,a) \mid a \in A }

\begin{align*} D_{R^{-1}} &= G_R \ G_{R^{-1}} &= D_R \end{align*}

\begin{align*} R_1^{-1} &= {(a,1),(a,2),(a,3),(a,4)}\ R_2^{-1} &= {(a,1),(b,2),(c,3)}\ R_3^{-1} &= {(c,2),(b,3),(a,4)}\ R_4^{-1} &= {(j,j),(k,k),(l,l)}\ R_5^{-1} &= {(k,j),(l,k),(j,l)}\ R_6^{-1}&= {(j,k),(j,l),(k,j),(k,l),(l,j),(l,k) }\ R_7^{-1} &= {(l,j),(k,j),(l,k)} \end{align*}

Quiz