select the best translation into predicate logic, using the following translation key:
d: Diego
s: Sean
Dx: x is on the Dean's list
Px: x is a philosophy major
Sx: x is a student
Vx: x is a valedictorian
-There are exactly two philosophy majors on the Dean's list.
A) Pd • Ps • Dd • Ds
B) (∃x)(∀y)[(Px • Py • Dx • Dy) ⊃ x=y]
C) (∀x)(∀y)(∀z)[(Px • Py • Pz • Dx • Dy • Dz) ⊃ (x =y $ \lor $ x=z $ \lor $ y=z)]
D) (∃x)(∃y){Px • Dx • Py • Dy • x≠y • (∀z)[(Pz • Dz) ⊃ (z=x $ \lor $ z=y)]}
E) ~(∃x)(∃y)(∃z)(Px • Py • Pz • Dx • Dy • Dz • x≠y • x≠z • y≠z)

Question

select the best translation into predicate logic, using the following translation key: 
d: Diego
s: Sean
Dx: x is on the Dean's list 
Px: x is a philosophy major 
Sx: x is a student
Vx: x is a valedictorian
-There are exactly two philosophy majors on the Dean's list.
A) Pd • Ps • Dd • Ds
B) (∃x)(∀y)[(Px • Py • Dx • Dy) ⊃ x=y]
C) (∀x)(∀y)(∀z)[(Px • Py • Pz • Dx • Dy • Dz) ⊃ (x =y $ \lor $ x=z $ \lor $ y=z)]
D) (∃x)(∃y){Px • Dx • Py • Dy • x≠y • (∀z)[(Pz • Dz) ⊃ (z=x $ \lor $ z=y)]}
E) ~(∃x)(∃y)(∃z)(Px • Py • Pz • Dx • Dy • Dz • x≠y • x≠z • y≠z)

Quizplus · Accepted Answer

Option D translates to "There exist two distinct individuals x and y such that x and y are philosophy majors on the Dean's list, and for any individual z, if z is both a philosophy major and on the Dean's list, then z must be either x or y." This accurately represents the statement "there are exactly two philosophy majors on the Dean's list." None of the other options capture the idea of exactly two individuals meeting the criteria.

Select the Best Translation into Predicate Logic, Using the Following ∨ \lor ∨

Select the Best Translation into Predicate Logic, Using the Following $\lor$