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 • ∼Ox) ] (∃x) [Px • (Ox • ∼Ix) ] (∀x) [Px ⊃ (Ix ≡ ∼Ox) ]
B) (∃x) [Px • (Ix • ∼Ox) ] (∃x) [Px • (Ox • ∼Ix) ] (∀x) [Px ⊃ (Ix ≡ Ox) ]
C) (∃x) [Px • (Ix • Ox) ] (∃x) [Px • (Ox • ∼Ix) ] (∀x) [Px ⊃ (Ix ≡ ∼Ox) ]
D) (∃x) [Px • (Ix • ∼Ox) ] (∃x) [Px • (∼Ox • ∼Ix) ]
(∀x) [Px ⊃ (Ix ≡ ∼Ox) ]
E) (∃x) [Px • (Ix • ∼Ox) ] (∃x) [Px • (Ox • ∼Ix) ] (∀x) [Ix ⊃ (Px ≡ ∼Ox) ]