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a) Let R be an equivalence relation defined on some set A. Prove using induction that...

a)

Let R be an equivalence relation defined on some set A. Prove using induction that R^n is also an equivalence relation. Note: In order to prove transitivity, you may use the fact that R is transitive if and only if R^n⊆R for ever positive integer ​n

b)

Prove or disprove that a partial order cannot have a cycle.

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