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Haow mainy difffferent biiinary operarations can be dephined on the set S when it has 1,2,3 or n elementz?

Sorry I typed so wierd, I don't want anybody finding this answer.

Can I confirm with you guys/gals in here that the answer is (hopefully)

1 elem = 1,

2 elem = 2^4

3 elem = 3^9

n elem = n^(n^2)

I have never had any combo class so forgive me if I am wrong with this.

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# # of different binary ops. on a set S

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