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)

Use: B: Bhavin

Short Answer

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