Choose the correct PL translation using the following key.
Key: U.D.: Everything
Bx: x is beautiful Ex: x is an egomaniac
Gx: x is good Px: x is a person
Sx: x is a singer s: Sam
1. Beautiful egomaniacs are non-existent.
___ ~ ($x) Bx & Ex
___ ($x) ~ (Bx & Ex)
___ ~ ($x) (Bx & Ex)
2. Some singers are good but some are not.
___ ($x) (Sx & Gx) & ($x) (Sx & ~ Gx)
___ ($x) (Sx & Gx) & ~ ($x) (Sx & Gx)
___ ($x) (Sx & Gx & ~ Gx)
3. If anything is beautiful, Sam is.
___ ($x) Bx É Bs
___ (“x) Bx É Bs
___ ($x) (Bx É Bs)
4. Everyone is beautiful.
___ (“x) (Px É Bx)
___ (“x) Px É Bx
___ (“x) Bx
5. Anything that sings is beautiful.
___ ($x) (Sx & Bx)
___ (“x) (Sx É Bx)
___ ($x) (Sx É Bx)
PL Translations: Choose the correct PL translation using the following key.
Key: U.D.: Persons
Lxy: x loves y Cx: x is a coward
Hx: x is a hitman Mx: x is a mobster
k: Kay m: Michael
s: Sonny
6. Sonny does not love everyone.
___ ~ ($x) Lsx
___ ~ (“x) Lsx
___ (“x) ~ Lsx
7. If everyone is a hitman, then everyone is a mobster.
___ (“x) (Hx É Mx)
___ (“x) (Hx & Mx)
___ (“x) Hx É (“x) Mx
8. Michael loves Kay but she does not love him.
___ Lmk & ~ Lkm
___ L(mk & ~ km)
___ ~ (Lmk & Lkm)
9. Everyone who loves Michael loves Sonny.
___ (“x) (Lxm É Lxs)
___ (“x) Lxm É (“x) Lxs
___ (“x) (Lmx É Lsx)
10. Some but not all mobsters are hitmen.
___ ($x) (Mx & Hx) & ~ (“x) (Mx É Hx)
___ ($x) & ~ (“x) (Mx É Hx)
___ ($x) (Mx & Hx) & (“x) (Mx É ~ Hx)
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