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) Pa • ∼Pb
Ia • ∼Id
B) Pa • ∼Pd
∼Ia • ∼Id
C) Pa • ∼Pd
Oa • ∼Id
D) Pa • ∼Pd
Ob • Od
E) Pa • ∼Pd
Ia • ∼Id

Question

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) Pa • ∼Pb
Ia • ∼Id
B) Pa • ∼Pd
∼Ia • ∼Id
C) Pa • ∼Pd
Oa • ∼Id
D) Pa • ∼Pd
Ob • Od
E) Pa • ∼Pd
Ia • ∼Id

Quizplus · Accepted Answer

In option E, Pa • ∼Pd means that Mercury is present and Pluto is absent. Ia • ∼Id means that both Mercury and Venus are present and Pluto is absent, which is true based on the given assignments. Thus, option E is the correct theory modeled by the interpretation.

Consider the Following Domain, Assignment of Objects in the Domain