I am having trouble with the following question:
Relations $S$ and $R$ are defined on the set $$\{1, 2, 3, \ldots, 12\}$$
as follows: $$R = \{(x, y)\mid xy = 12\}$$ $$S = \{(x, y)\mid 2x = 3y\}$$
So far I have resolved the composite matrix S o R to be:
{(3,6),(6,3),(9,2)}
Would the logical boolean matrix therefore look the following?
What you've written is fine, for those values, but it tells us nothing about the truth value of $(1, 2)$ with respect to $S\circ R$. So I would add that for $x \in S$, you expand your answer (words will do). E.g.,
Putting $U = \{1, 2, 3, \ldots, 11, 12\}$:
Then for all $x \in U, \;x \notin \{3, 6, 9\}$, for all $y \in U$, $(x, y)\notin S\circ R$, i.e., $\operatorname{boolean}(x, y) = F$