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
-At most two philosophy majors are on the Dean's list.
A) (∃x)(∃y){Px • Dx • Py • Dy • (∀z)[(Pz • Dz) ⊃ (x=z $ \lor $ y=z)]}
B) (∃x)(∃y)[Px • Dx • Py • Dy • ~(∃z)(Pz • Dz • x=z • y=z)]
C) (∀x)(∀y)(∀z)(Px • Dx • Py • Dy • Pz • Dz • x≠y • x≠z • y≠z)
D) ~(∃x)(∃y)(∃z)(Px • Dx • Py • Dy • Pz • Dz • x≠y • x≠z • y≠z)
E) (∀x)(∀y)(∀z)[(Px • Dx • Py • Dy • Pz • Dz) ⊃ (x=y $ \lor $ x=z $ \lor $ 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
-At most two philosophy majors are on the Dean's list.
A) (∃x)(∃y){Px • Dx • Py • Dy • (∀z)[(Pz • Dz) ⊃ (x=z $ \lor $ y=z)]}
B) (∃x)(∃y)[Px • Dx • Py • Dy • ~(∃z)(Pz • Dz • x=z • y=z)]
C) (∀x)(∀y)(∀z)(Px • Dx • Py • Dy • Pz • Dz • x≠y • x≠z • y≠z)
D) ~(∃x)(∃y)(∃z)(Px • Dx • Py • Dy • Pz • Dz • x≠y • x≠z • y≠z)
E) (∀x)(∀y)(∀z)[(Px • Dx • Py • Dy • Pz • Dz) ⊃ (x=y $ \lor $ x=z $ \lor $ y=z)]

Quizplus · Accepted Answer

The statement "At most two philosophy majors are on the Dean's list" means that if there are three philosophy majors on the Dean's list, then at least two of them must be the same person. This is captured by option E, which states that if x, y, and z are all philosophy majors on the Dean's list, then at least two of them must be the same (x=y or x=z or y=z).

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

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