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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?

enter image description here

amWhy
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user3371750
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  • Well, you need to completely define the matrix (that is, false everywhere except for the three entries above), but otherwise you are correct. – copper.hat Jul 07 '14 at 20:11

1 Answers1

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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., $\operatorname{boolean}(x, y) = F$

amWhy
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