If there are any guards, then if none of the prisoners escape, then they will be rewarded.
A) (x){[Gx ⊃(y)(Py ⊃ ∼Ey)] ⊃ Rx}
B) (x){Gx ⊃ [(∃y)(Py • ∼Ey) ⊃ Rx]}
C) (∃x)Gx ⊃ [(y)(Py ⊃ ∼Ey) ⊃ Rx]
D) (x){Gx ⊃ [(y)(Py ⊃ ∼Ey) ⊃ Rx]}
E) (∃x){Gx • [(y)(Py ⊃ ∼Ey) ⊃ Rx]}

Question

Quizplus · Accepted Answer

The statement begins with "If there are any guards," which can be symbolized as (x)Gx. The statement "none of the prisoners escape" can be symbolized as (y)(Py ⊃ ∼Ey). Finally, the statement "they will be rewarded" can be symbolized as Rx.

Putting it all together, we get: (x){Gx ⊃ [(y)(Py ⊃ ∼Ey) ⊃ Rx]}. This is exactly what is represented in option D.

If There Are Any Guards, Then If None of the Prisoners