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R = {(a,a),(a,c),(a,d),(b,b),(b,a),(c,c),(c,b),(c,d),(d,e),(e,a)}

I believe it is transitive however in the answer sheet I have it says it is not.

I'm following the idea that if R(a,b) and R(b,c) then if R(a,c) it is transitive.

I have tried this with respect to the above:

There is R(a,c) & R(c,d). There is also (a,d). Would this not mean that it is transitive? Thanks

Nik F
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    I see that $a\sim c$ and also that $c\sim b$. What should this imply if the relation was in fact transitive? Since that's not the case, what does this mean about the relation? – JMoravitz Nov 15 '16 at 20:21
  • It's not just ab and bc. It has to be every combo. Note. aRc and cRb nut there is no aRb. There's also aRd and dDe but no aRe. There is bRa and aRc but no bRc, etc. This is very much not transitive. – fleablood Nov 15 '16 at 21:10

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Yes, that would mean that the relation is transitive, but it would have to hold for every possible duo of pairs. For instance, note that $R(c,d)$ and $R(d,e)$, but $\not R(c,e)$. Therefore the relation is not transitive.

Arthur
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