Consider the Following Domain, Assignment of Objects in the Domain

Multiple Choice

consider the following domain, assignment of objects in the domain, and assignments sets to predicates.
Domain = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto}
P = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}
I = {Mercury, Venus}
O = {Mars, Jupiter, Saturn, Uranus, Neptune}
a = Mercury b = Jupiter c = Saturn
d = Pluto
-Given the customary truth tables, which of the following theories is modeled by the above interpretation?

A) (∃x) (∼Px • Ix)
(∃x) ∼Px
B) (∃x) (Px • ∼Ix) (∃x) ∼Px
C) (∃x) (Px • Ix)
(∀x) (Px ⊃ Ix)
D) (∃x) (Ox • Ix)
(∃x) ∼Px
E) (∃x) (Ox • ∼Px) (∀x) (Ix ⊃ Px)