Formulas & Sentences of PL...

Hi again everyone,

OK, so I have some more problems I have been working on and I want to
make sure I have them right. I have an exam in two days and need to egt
this down perfect. I will type the problems and my answers. Please
check them and if any are wrong, please tell me why so I know better
next time.

On this first part I am trying to say which of the following are
FORMULAS of PL:

a. (Allx)Faa
I said NO, because they have the (Allx) there and there is no x in the
formula. correct?

b. (Ex)((Fx & Gxy) Horseshoe (Ally)Hxy))
Yes, this is a formula

c. (Ex)((Fx & Gxy) horseshoe (Allx)Hxy))
No, because of overlapping scopes

d. (Allx)((Ey)Fyx horseshoe (Ey)Fxy)
yes, this is a formula

e. Fx horseshoe (Ex)Fx
yes, this is a formula


Ok, on these next ones I'm trying to determin if they are SENTENCES of
PL:

a. (Allx)(Fx horseshoe Gx)
yes

b. (Allx)Fx horseshoe Gx
no, because the scope of (Allx) doesn't reach the last x in Gx?

c. (Allx)(Fx & Gx) horseshoe (Ex)Hxy
I said no, this is not a sentence because we have y out at the end with
no (Ally) or (Ey) attached?

d. (Allx)(Fx & (Ally)Gxy) horseshoe (Ex)Hxy
No, because at the end we have (Ex)Hxy, but no quantifier for the y.

e. (Allx)(Fx & (Ally)Gxy) horseshoe (Ex)(Ally)Hxy
yes?

Thanks!

.