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I'm trying to prove to myself that the order of full outer joins doesn't matter, but, in an abstract sense, I'm coming up with nothing.

How would one go about proving that the order of a set of FULL OUTER JOINs that are executed to turn many tables into a single table does not affect the result set (i.e., prove commutativity and associativity of the FULL OUTER JOIN operation)?

I have searched online and saw that fullouterjoin are both commutative and associative and these are their equations:

associative-> R fullouterjoin (S fullouterjoin K) = (R fullouterjoin S) fullouterjoin K

commutative-> R fullouterjoin S = S fullouterjoin R

But i am having hard time showing how this is true by either a counterexample or a prove!! Can someone explain

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