All Philosophers Respect Each Other $\lor$ Ix)] / (∃X)(Ox • Ix)
B) 1

Multiple Choice

All philosophers respect each other. Some philosopher doesn't study some philosopher. Anything which respects something without studying it is open-minded, if ignorant. So something is open-minded and ignorant. (Ix: x is ignorant; Ox: x is open-minded; Px: x is a philosoper; Rxy: x respects y; Sxy: x studies y)
-Which of the following is the best translation into F of this argument?

A) 1. (∀x) (∀y) [(Px • Py) ⊃ (Rxx • Ryy) ] 2. (∃x) (∃y) [(Px • Py) • ~Sxy]
3) (∀x) (∀y) [(Rxy • ~Sxy) ⊃ (Ox $\lor$ Ix) ] / (∃x) (Ox • Ix)
B) 1. (∀x) (∀y) [(Px • Py) ⊃ (Rxy ≡ Ryx) ] 2. (∃x) (∃y) [(Px • Py) • ~Sxy]
3) (∀x) (∀y) [(Rxy • ~Sxy) ⊃ (Ox $\lor$ Ix) ] / (∃x) (Ox • Ix)
C) 1. (∀x) (∀y) [(Px • Py) ⊃ (Rxy • Ryx) ] 2. (∃x) (∃y) [(Px • Py) • ~Sxy]
3) (∀x) (∀y) [(Rxy • ~Sxy) ⊃ (Ox $\lor$ Ix) ] / (∃x) (Ox • Ix)
D) 1. (∀x) (∀y) [(Px • Py) ⊃ (Rxy • Ryx) ] 2. (∃x) [Px • (∃y) (Py • ∼Sxy) ]
3) (∀x) (∀y) [(Rxy • ∼Sxy) ⊃ (Ox • Ix) ] / (∃x) (Ox • Ix)
E) 1. (∀x) (∀y) [(Px • Py) ⊃ (Rxx • Ryy) ] 2. (∃x) (∃y) [(Px • Py) • ~Sxy]
3) (∀x) (∀y) [(Rxy • ~Sxy) ⊃ (Ox $\lor$ Ix) ] / (∃x) (Ox $\lor$ Ix)