If I have no creatures in the graveyard, do I nevertheless have one Type of creature?

I have a card called Solidarity, reading:

If you have only 1 original Type of monster in your Graveyard, face-up monsters you control with the same Type gain 800 ATK.

In the case where the graveyard has two or more creatures of the same type then it's obvious we can use the effect; similarly, if the graveyard has precisely one creature in it, then it has exactly one type of creature in it (and so the effect may be applied).

But if the graveyard has no creatures in it, I would argue that there is exactly one type of creature in it (this is a vacuous truth). I wanted to use the card in this situation but my opponent absolutely refused it.

To me this truth is as valid as saying the Empty Set is Hausdorff. I'm hoping there are mathematicians out there that also play Yugioh and are qualified to answer this; alternatively, I am hoping there is an official answer to this, not just some opinions.

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Your premise is faulty - this is not a vacuous truth. If your graveyard is empty, the set of creature types of creatures in your graveyard is also empty. That empty set has zero elements, not one. Vacuous truth is still truth, but your example is not such a case. If the card said "if all creatures in your graveyard are the same type", then you'd have a real question. – Jefromi Jun 21 '13 at 19:44
-1 for not linking the specific card in mind, AND for tagging this with both MTG and Yu-gi-oh. Since this you're talking about a scenario in yugioh, MTG rulings don't apply. – Sam I am Jun 21 '13 at 19:51
If you improve the question, I'll undownvote – Sam I am Jun 21 '13 at 19:51
Also, I don't know about Yu-Gi-Oh rules, but with Magic, rules questions are definitely best served by specific examples. The rules are complex, detailed, but generally clear - as long as you actually have a specific situation to apply them to. Given this, you probably should not be asking about both games. You want to look at actual cards and actual rules. – Jefromi Jun 21 '13 at 19:52
@Squirtle No, we're downvoting because (as it says when you hover over it) the question is unclear or not useful. If this bothers you, it's because you are taking the reputation system seriously. – Jefromi Jun 21 '13 at 20:59