Let * be a binary operation on a nonempty set X and let Y be a nonempty subset of X and be a family of nonempty subsets of X. Prove that:

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- Aug 26th 2008, 12:59 PMtttcomraderFamily of subset problem
Let * be a binary operation on a nonempty set X and let Y be a nonempty subset of X and be a family of nonempty subsets of X. Prove that:

- Aug 26th 2008, 01:23 PMPlato

That is one direction. Can you use it to do the other direction?

**I hope that I understand the notation you are using.**

If this is incorrect, please tell us what is correct. - Sep 7th 2008, 01:43 PMtttcomrader
For the opposite direction, I have:

Let

Then there exist an element such that

So then

Implies that

Thus complete the proof. I hope this is right.

There is a second part of the problem:

Prove that at least one of and holds, but they don't have to equal.

Now, so that means I would have two cases. But what gives me trouble is that what two different cases would give me those two different result? Would it be that and ?