I just wanted a little bit of guidance on how to work out this question in finding the boolean matrix of a relation :
Consider the following Hasse diagram of a partial ordering relation $S$ on the set $\{a,b,c,d,e,f\}$...
"Write down the Boolean matrix of relation S.."
Thank you.
The matrix representation of a relation $S$ from a set $X = \{x_1,x_2,\dots\}$ to a set $Y = \{y_1,y_2,\dots\}$ is given by the matrix $M$ where $$M_{i,j} = \begin{cases}1 & \text{if } (x_i,y_j) \in S\\ 0 & \text{if } (x_i,y_j) \notin S\end{cases}$$
Since you have six elements in your set, you will get a $6 \times 6$ matrix. From your diagram, we see that e.g. $(a,e) \in S$, so $M_{a,e} = 1$, but $(c,e) \notin S$, so $M_{a,c} = 0$. Also notice that since your relation is reflexive, it will have all $1$s on the diagional.