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While studying about binary relations, I got confused while solving some simple problems. For example: Let $R=\{(a,a), (a,c), (b,b), (b,c), (c,c), (c,a), (c,b), (d,d)\}$ be a binary relation on the set $A=\{a, b, c, d\}$

Are $\{(a,c), (c,a)\}$ and $\{(b,c), (c,b)\}$ enough to meet the criterion of symmetry or all combinations of $a$, $b$, $c$ and $d$ must be present for that? Respectively, is $\{(a,c), (c,b)\}$ enough to meet the criterion of transitivity?

Javi
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Glauvus
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1 Answers1

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The laws involved in defining binary relations are universal laws. It means that you have to verify them for ALL the elements on which the binary relation $R$ is defined.

For example regarding symmetry, for any couple $(x,y) \in R$, you have to verify that $(y,x)$ is also belonging to $R$. This is the case in your example. Apply the same verifications for reflexivity and transitivity.

mathcounterexamples.net
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