Would anyone be able to help me answer this question?
Let $A=\{1,2,3,4,5\}$ and $R$ be the relation on the set $A$ whose matrix is $$M_R = \begin{bmatrix}1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 0 & 0\end{bmatrix}$$ Determine whether $R$ is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. If the relation fails to have a property, give an example showing why it fails in this case.
