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 is exactly one philosophy major on the Dean's list.
A) (∃x){(Px • Dx) • (∀y)[(Py • Dy) ⊃ y=x]}
B) (Pd • Ps) ⊃ [(Dd $ \lor $ Ds) • ~(Dd • Ds)]
C) (∀x)(∀y){[(Px • Dx) • (Py • Dy)] ⊃ x=y}
D) (∃x){(Px • Dx) ⊃ (∀y)[(Py • Dy) ⊃ x=y]}
E) (Pd • Dd) $ \lor $ (Ps • Ds)

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 is exactly one philosophy major on the Dean's list.
A) (∃x){(Px • Dx) • (∀y)[(Py • Dy) ⊃ y=x]}
B) (Pd • Ps) ⊃ [(Dd $ \lor $ Ds) • ~(Dd • Ds)]
C) (∀x)(∀y){[(Px • Dx) • (Py • Dy)] ⊃ x=y}
D) (∃x){(Px • Dx) ⊃ (∀y)[(Py • Dy) ⊃ x=y]}
E) (Pd • Dd) $ \lor $ (Ps • Ds)

Quizplus · Accepted Answer

This statement reads "there exists exactly one x such that x is a philosophy major on the Dean's list, and for all y, if y is a philosophy major on the Dean's list, then y is that same x." This can be translated as (∃x){(Px • Dx) • (∀y)[(Py • Dy) ⊃ y=x]} in predicate logic. The other options do not accurately capture the meaning of the English sentence or contain unnecessary complexities.

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

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