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 = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto}
a = Mercury b = Jupiter c = Saturn d = Pluto
Mx = {Mercury, Mars}
Px = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}
Cxy = {, , , , , , , , , ,
, , , , , , , , , , , , , , , , , , , , , , , , , }
-Given the customary truth tables, which of the following theories is modeled by the above interpretation?

A) (∀x) (Px ⊃ Mx)
~(∃x) Px
(∀x) (∀y) [(Px • Py) ⊃ Cxy]
B) (∀x) (Mx ≡ Px)
~(∀x) Mx (∀x) [(∀y) Cxy ⊃ Py]
C) (∀x) (Mx $\lor$ Px)
~(∃x) Mx
(∀x) [Px ⊃ ~(∀y) (Py ⊃ Cxy) ]
D) (∀x) (~Mx $\lor$ Px)
~(∀x) (Px
(∀x) [Px ⊃ (∀y) (Py ⊃ Cxy) ]
E) (∀x) (Mx ⊃ Px)
∼(∀x) Px
(∀x) [∼Px ⊃ (∀y) (Py ⊃ Cyx) ]

Correct Answer:

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