So here's a problem. State Driver's License applications often ask this question:
"Do you have a license from more than one state?"
We all take that to mean "Do you own more than one license from two different states?" but that's not what the question actually says. In Mathematical notation:
(∃L)(∃S1)(∃S2)[(S1 != S2)^From(L,S1)^From(L,S2)]
This is the literal meaning of those words. And it reads as follows: There exists a License such that it has Properties (State 1) and (State 2); these properties are different.
The less formal reading: There exists a license from two different states.
That's one license. Singular. From two different states. (or more is just left off because it's just the range (S1..Sn) )
This is obviously always False. What they're asking you is if you own something that does not exist. Licenses are not printed with more than one state on them. So you should always say False on this question in a strict sense.
What they meant to say is:
(∃L1)(∃L2)(∃S1)(∃S2)[(S1 != S2)^(L1!=L2)^From(L1,S1)^From(L2,S2)]
There exists two licenses with different properties State such that neither license is from the same state and no License has more than one state.
This is a problem because driver's licenses are legal documents. If you did ever answer False on that statement and were thrown into court for it, you could potentially hire a lawyer to call a mathematician in as an expert witness to testify that the second form is how the question should've been worded and that your answer was correct given the wording of the question.
Here's a key to help understand this:
∃ means "there exists"
!= is inequality or "different than"
^ is AND meaning "all of these statements must be True" such as "You need cake AND presents to have a party". You only have a party if you have both cake and presents.
From is just transference from the sentence above. It's not mathematical.
So why is this important? Because Vanguard just had that problem recently with the Lord keyword. The translation we got suggested that:
If there exists a card C that has property NOT same-clan S, then this unit U can NOT attack.
Written formally this is:
(∃C)(∃S)[(S != S) ∴ U ¬ attack]
That's true if you have any card that isn't the same clan. Any C that does not have property NOT S. It satisfies the condition that object C with property NOT S can NOT attack. Therefore it is true. But the problem is that this isn't what it was supposed to say. What it was supposed to say was more like:
If NOT for all cards C1..Cn rear-guard positions R, they have the property same-clan S, then this unit U can NOT attack.
Which looks more like:
¬(∀C in R) [(S = S) ∴ U ¬ attack]
This is true if no cards have the same clan. If no C have property S, it can NOT attack. (This also has a bizarre consequence that if there are no cards C at all, it doesn't satisfy this NOT condition and therefore it can still attack.)
We found out the latter is actually how it's worded (from Bushiroad). Hopefully the English isn't so ambiguous when it is printed.
∀ means "for all"
∴ means "therefore" or "it follows"
¬ means "not". I could also use ! but I wanted to keep that separate from inequality.
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