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}
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 ⊃ [(∃y) Cxy • (∃y) Cyx]} Cab • ~Cba
Cca • ~Cac Cad • ~Cda
B) (∀x) {Px ⊃ [(∃y) Cxy ≡ (∃x) Cyx]} Cab • ~Cba
Cac • ~Cca Cad • ~Cda
C) (∀x) [Px ⊃ (∃y) (Cxy • Cyx) ] Cba • ~Caa
Cca • ~Ccc Cda • ~Cdd
D) (∀x) {Px ⊃ [(∃y) Cxy $\lor$ (∃y) Cyx]}
Cab • ∼Cba Cac • ∼Cca Cad • ∼Cda
E) (∀x) [Px ⊃ (∃y) (Cxy $\lor$ Cyx) ]
Cab • ~Cba Cac • Cad
~(~Cca • ~Cda)