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

consider the following domain, assignment of objects in the domain, and assignments sets to predicates.
Domain = {1, 2, 3, ..., 28, 29, 30}
N = {1, 2, 3, ..., 28, 29, 30}
E = {2, 4, 6, ..., 28, 30}
O = {1, 3, 5, ..., 27, 29}
P = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
a = 1
b = 2
c = 28
-Given the customary truth tables, which of the following theories is modeled by the above interpretation?

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

Correct Answer:

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