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}
a = 1
e = 21
b = 2
f = 23
c = 4
g = 27
d = 20
h = 29
Ex = {2, 4, 6, ..., 28, 30}
Ox = {1, 3, 5, ..., 27, 29}
Px = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
Sxyz = The set of all triples such that the first is the sum of the second and third
{<2, 1, 1>, <3, 1, 2>, <3, 2, 1>, <4, 1, 3>, <4, 2, 2>, <4, 3, 1>, <5, 1, 4>, ... }
-Given the customary truth tables, which of the following theories is modeled by the above interpretation?

A) (∃x) (∃y) [(Ex • Ey) • Sfxy] (∃x) (∃y) [(Ox • Oy) • Sfxy]
(∀x) {Ex ⊃ {(∃y) (∃z) [(Ey • Ez) • Sxyz) ] $\lor$ (∃y) (∃z) [(Ox • Oy) • Sxyz]}}
B) (∃x) (∃y) [(Ex • Ey) • Sdxy]
(∃x) (∃y) [(Ox • Oy) • Sdxy]
(∀x) {Ex ⊃ {(∃y) (∃z) [(Ey • Ez) • Sxyz) ] $\lor$ (∃y) (∃z) [(Ox • Oy) • Sxyz]}}
C) (∃x) (∃y) [(Ex • Ey) • Sdxy]
(∃x) (∃y) [(Ox • Oy) • Sdxy]
(∀x) {Ex ⊃ {(∃y) (∃z) [(Ey • Ez) • Sxyz) ] • (∃y) (∃z) [(Ox • Oy) • Sxyz]}}
D) (∃x) (∃y) [(Ex • Ey) • Sfxy]
(∃x) (∃y) [(Ox • Oy) • Sfxy]
(∀x) {Ex ⊃ {(∃y) (∃z) [(Ey • Ez) • Sxyz) ] • (∃y) (∃z) [(Ox • Oy) • Sxyz]}}
E) (∃x) (∃y) [(Ex • Ey) • Sdxy]
(∃x) (∃y) [(Ox • Oy) • Sdxy]
(∀x) {Ox ⊃ {(∃y) (∃z) [(Ey • Ez) • Sxyz) ] $\lor$ (∃y) (∃z) [(Ox • Oy) • Sxyz]}}

Correct Answer:

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