Consider the Following Domain, Assignment of Objects in the Domain $\lor$

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