select the best English interpretation of the given statements of predicate logic.
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused
Rx: x is loved
Sx: x will fetch balls
Tx: x will fetch sticks.
-(∃x)[Px • (∼Qx • Rx)] ⊃ (∀x)[(Px • Rx) ⊃ Tx)]
A) If some poodles are neither abused nor loved, then all loved poodles will fetch sticks.
B) If some poodles are not abused but are loved, then all loved poodles will fetch sticks.
C) Some poodles are neither abused nor loved, and all loved poodles will fetch sticks.
D) Some poodles are abused and unloved, but all loved poodles will fetch sticks.

Question

select the best English interpretation of the given statements of predicate logic. 
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused 
Rx: x is loved
Sx: x will fetch balls 
Tx: x will fetch sticks.
-(∃x)[Px • (∼Qx • Rx)] ⊃ (∀x)[(Px • Rx) ⊃ Tx)]
A) If some poodles are neither abused nor loved, then all loved poodles will fetch sticks.
B) If some poodles are not abused but are loved, then all loved poodles will fetch sticks.
C) Some poodles are neither abused nor loved, and all loved poodles will fetch sticks.
D) Some poodles are abused and unloved, but all loved poodles will fetch sticks.

Quizplus · Accepted Answer

The statement is a conditional statement where the antecedent is (∃x)[Px • (∼Qx • Rx)] which translates to "There exists a poodle that is not abused and loved". The consequent is (∀x)[(Px • Rx) ⊃ Tx)] which translates to "For all poodles that are loved and not abused, they will fetch sticks". Therefore, the best interpretation is "If some poodles are not abused but are loved, then all loved poodles will fetch sticks", which is logically equivalent to the given statement.

Select the Best English Interpretation of the Given Statements of Predicate