Probably pretty simple for ya'll but

[kshan5]

So I just got out of my intro to logic final at UMass and there was one question I just couldn't solve, and I'd like to know how. Anyways, here it is,

1. ∀xFx V ∀xGx
2. Show: ∀x(Fx V Gx)


I did 90% of the exam in a half hour, then spent the next hour on this alone and couldn't really get that close. Anyways, just really curious how you'd go about doing it.

Thanks.

 

[JSuarez]

Show how? By using the quantifier's semantic definitions or were you asked to use a particular proof system? Anyway, in the former, here's a hint: what must happen for the conclusion to be false?