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

question 141

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)

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