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Prove the Transitive Theory

Prove the following theory:

1) R1 is a subset of R2 => All of R3, R1R3 is a subset of R2R3 and
2) R1 is a subset of R2 => All of n, (R1)^n is a subset (R2)^n
3) Suppose R is transitive, then for all of n, R^n is a subset of R.

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Solution Summary

A transitive theory is proven. The solution is detailed and well presented.

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