Prove the following $(R\cap S)^n=R^n \cap S^n$

Asked Jan 18 '14 at 14:58

Active Jan 18 '14 at 14:58

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I would like to prove the following without induction. $$(R\cap S)^n=R^n \cap S^n$$ We can start by take $(a,b)\in (R\cap S)^n$ its represent a path from $a$ to $b$ right?
Any hints? Thanks.

asked Jan 18 '14 at 14:58

Ofir Attia

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You can use induction and use the fact that intersection is commutative. – Spock Jan 18 '14 at 15:04
I know how to prove it with induction, I asked without – Ofir Attia Jan 18 '14 at 15:05
My bad. I'm sorry. – Spock Jan 18 '14 at 15:10

Prove the following $(R\cap S)^n=R^n \cap S^n$

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