Topic: Combining relations (Composition of relations)

Question

Let R be a relation.

Why $R^2 oR^2 !=R^4$ while $R^3 oR =R^4$?

Please explain.

Comments

Can you give an example where $R^2 \circ R^2 \neq R^4 \ ?$

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I am trying to find that out only. But I don’t know I got know in a video I am referring through the course.

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Composition of relations is associative. You can check here

It means, $R \circ (S \circ T)  = (R \circ S) \circ T$

So, here, $R^4 = R^3 \circ R = (R^2 \circ R) \circ R = R^2 \circ (R \circ R) = R^2 \circ R^2$

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Thank you