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
-All philosophy majors except Sean are on the Dean's list.
A) (∃x)(Px • Dx • x≠s)
B) Ps • ∼Ds • (∀x)[(Px • x≠s) ⊃ Dx]
C) (∀x)[Dx ⊃ (Px ⊃ x≠s)]
D) (∀x)(Px ⊃ Dx) • Ps • ~Ds
E) (∀x)[Px ⊃ (Dx ⊃ x≠s)]

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
-All philosophy majors except Sean are on the Dean's list.
A) (∃x)(Px • Dx • x≠s)
B) Ps • ∼Ds • (∀x)[(Px • x≠s) ⊃ Dx]
C) (∀x)[Dx ⊃ (Px ⊃ x≠s)]
D) (∀x)(Px ⊃ Dx) • Ps • ~Ds
E) (∀x)[Px ⊃ (Dx ⊃ x≠s)]

Quizplus · Accepted Answer

The statement "All philosophy majors except Sean are on the Dean's list" can be translated as "For all x, if x is a philosophy major and x is not Sean, then x is on the Dean's list." Using the provided translation key, this can be written as: (∀x)[(Px ∧ x≠s) → Dx]. This matches exactly with option B when we apply the conditional equivalence: [(p → q) ≡ (~p ∨ q)] and DeMorgan's law: ~(p ∧ q) ≡ ~p ∨ ~q.

Select the Best Translation into Predicate Logic, Using the Following