$,\{\begin{array}{c}\text{:}[x]\\ y\\ z\end{array}([1,0,1,0],[0,0,0,0],[1,0,1,0],[0,0,0,1])$

How can we quickly determine whether a relation $R$ is

antisymmetric by examining the matrix of $R($relative to

some ordering$)?$

Tell whether the relation of Exercise $10$ is reflexive, sym$-$

metric, transitive, antisymmetric, a partial order, and$/$or an

equivalence relation.