Symbolize the following sentences in PLE (predicate logic, in addition to the identity predicate) using the symbolization key:

UD: People
Sx: x is a sailor
Sxy: x is a son of y
Dxy: x is a daughter of y
Wx: x is a Wilcox
d: Daniel Wilcox
j: Jacob Wilcox
r: Rebecca Wilcox

1. Every Wilcox except Daniel is the offspring of a sailor.
2. Rebecca Wilcox has at least one son who is a sailor.
3. There are two and only two sailors in the Wilcox family.

UD: People in Doreen’s hometown
Dxy: x is a daughter of y
Px: x is a physician
Oxy: x is older than y
Bx: x is a baseball player
Mxy: x is married to y
Mx: x is a marine biologist
d: Doreen
j: Jeremy

1. Doreen is a physician and so is her eldest daughter
2. The only baseball player in town is married to one of Jeremy’s daughters.

Show that each of the following is valid in PDE:

1. Ge ⊃ d = e
Ge ⊃ He
Therefore, Ge ⊃ Hd
2. (∃x)(Hx & Mx)
Ms & ~Hs
Therefore, (∃x)[(Hx & Mx) & ~x=s]

Show that the following is a theorem in PDE:
∀(x) ∀(y) ∀(z)[(x = y & y = z) ⊃ x = z]

Symbolize the following argument in PLE and show that it is valid in PDE:
Hyde killed some innocent person. But Jekyll is Hyde. Jekyll is a doctor. Hence, some doctor killed some innocent person.

Symbolize the following sentences in PLE (predicate logic, in addit...