Discrete Math - Relations and Matrix Representations Are these answers correct? Do we assume $p$ is created from $S$ twice?
Binary relation $p$ on the set $S = \{a,b,c,d,e\}$ is defined as: $￼p = \{(a,c),(a,e),(b,a),(e,d)\}$.
￼


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*What is the matrix representation of $p$?

*Is $p$ a reflexive relation? 


Please explain. ￼ 
(1.) Would the matrix representation of $p$ be following: a $1$ placed at the intersections of $(a,c), (a,e), (b, a), (e,d)$ and the rest zeros where $a-e$ is listed for columns and rows?
(2.) $p$ is not a reflexive relation because for every element $a$ in $A$, there is not an ordered pair $(a,a)$ in the relation.

In short, you've got the right ideas. The matrix representation for $p$ is 
$$\begin{array}{c|ccc}
&a&b&c&d&e\\ \hline
a&0&0&1&0&1\\
b&1&0&0&0&0\\
c&0&0&0&0&0\\
d&0&0&0&0&0\\
e&0&0&0&1&0
\end{array}$$
You are also correct that $p$ is not reflexive on $S$. For $p$ to be reflexive on $S$, all the entries of the main diagonal of the above matrix must be $1$. If any entry in the main diagonal is instead $0$, the relation is not reflexive on $S$.
