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

question 106

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

• A) (∃x)(Px • Ix) • (∃x)(Px • ∼Ix) (∀x)[Px ⊃ (Ix • Ox)]
• B) (∃x)(Ox • Ix) • (∃x)(Px • ∼Ix) (∀x)[Px ⊃ (Ix \( \lor \) Ox)]
• C) (∃x)(Px • Ix) • (∃x)(Px • ∼Ix) (∀x)[(Ix \( \lor \) Ox) ⊃ Px]
• D) (∃x)(Px • Ix) • (∃x)(Ix • ∼Px) (∀x)[Ix ⊃ (Px \( \lor \) Ox)]
• E) (∃x)(Px • Ix) • (∃x)(Ox • ∼Px) (∀x)[Ox ⊃ (Ix \( \lor \) Px)]

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