2

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: $p = \{(a,c),(a,e),(b,a),(e,d)\}$. 

  1. What is the matrix representation of $p$?
  2. 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.

Ken
  • 3,751
BostonMan
  • 89

1 Answers1

0

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 $S$.

Ken
  • 3,751