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I read that all binary relations are associative. i.e (p.q).r = p.(q.r). However, I was curious that does this hold if p,q, and r are ternary relationships. I tried several examples, such as the one below, but could not prove that ternary relationaships are NOT associate. So, are they associative or not

p = {(a,b,c) , (f,o,x)} q = { (f,d,e), (x,o,c) } r = { (e,t,o), (c,t,s)} 

The output for (p.q).r and p.(q.r) in both cases is {(f,o,o,t,s)}

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    What do you mean by "binary relation"?2012-11-02
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    I assume you're talking of composition of relations. I'm familiar with the binary case. How exactly are you defining the composition of ternary relations?2012-11-02
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    It is far not true that "all binary relations are associative". Probably it was meant: "*in the following, we assume* that all binary *operations* that will occur, is associative."2012-11-02
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    I know this is irrelevant to your question, but what do you mean that all binary relations are associative? Do you mean the composition of relations like $p.q= \left\{\left(x,y\right)|\exists z, \left(x, z\right) \in p , \left(z,y \right) \in q \right\}$? If yes, I don't know of any obvious analogue for composing ternary relations.2012-11-02
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    Yes, how do yoe mean the composition of *ternary relations*?2012-11-02
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    So. How did you get this 5-tuple $(f,o,o,t,s)$?2012-11-02

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