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

Multiple Choice

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]}