Question: Let R be a symmetric relation on set A. Show that [tex]R^n[/tex] is symetric for all positive integers n.(adsbygoogle = window.adsbygoogle || []).push({});

My "solution":

Suppose R is symmetric,

[tex]

\exists a,b \in A ((a,b) \in R \wedge (b,a) \in R)

[/tex]

For n=1,

[tex]R^1=R[/tex].

Next, assume that [tex] (a,b) and (b,a) \in R^k[/tex], for k a possitive integer. So [tex]R^{k+1}=R^k \circ R[/tex].

Then what?

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# Homework Help: Symmetric relation

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