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

question 19

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)

---

Definitions:

Scoliosis

A medical condition characterized by a sideways curvature of the spine, which can impact posture and movement.

Flexion

A movement that decreases the angle between two body parts, such as bending an elbow or knee.

Extension

The movement by which the angle between two bones is increased, typically referring to limbs or joints.

Circumduction

A circular movement of a limb or eye that combines flexion, extension, abduction, and adduction.