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) (Ma • Pb) • (Pc $\lor$ Pd) (∃x) Cxa • ~(∃x) Cxd
B) (Pa • Mb) • (Pc $\lor$ Pd) (∃x) Cxd $\lor$ ~(∃x) Cxa
C) (Pa • Pb) • (Pc $\lor$ Pd)
(∃x) Cxd • ∼(∃x) Cxa
D) (Pa • Pb) • (Mc $\lor$ Pd) (∃x) Cxd $\lor$ ~(∃x) Cxa
E) (Pa • Pb) • (Pc $\lor$ Md) (∃x) Cxa • ~(∃x) Cxd

Correct Answer:

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