Select the Best Translation into Predicate Logic, Using the Following $\lor$

question 106

Multiple Choice

select the best translation into predicate logic, using the following translation key:
d: Diego
s: Sean
Dx: x is on the Dean's list
Px: x is a philosophy major
Sx: x is a student
Vx: x is a valedictorian
-At least four philosophy majors are on the Dean's list.

• A) (∃x)(∃y)(∃z)(∃w)[Px • Dx • Py • Dy • Pz • Dz • Pw • Dw •
• (x=y \( \lor \) x=z \( \lor \) x=w \( \lor \) y=z \( \lor \) y=w \( \lor \) z=w)]
• B) (∀x)(∀y)(∀z)(∀w)[(Px • Py • Pz • Pw • Dx • Dy • Dz • Dw) ⊃
• (x=y \( \lor \) x=z \( \lor \) x=w \( \lor \) y=z \( \lor \) y=w \( \lor \) z=w)]
• C) (∃x)(∃y)(∃z)(∃w)(Px • Dx • Py • Dy • Pz • Dz • Pw • Dw • x≠y • x≠z • x≠w • y≠z • y≠w • z≠w)
• D) (∀x)(∀y)(∀z)(∀w)[(Px • Py • Pz • Pw • Dx • Dy • Dz • Dw) ⊃
• (x≠y • x≠z • x≠w • y≠z • y≠w • z≠w)]
• E) (∃x)(∃y)(∃z)(∃w)[(Px • Dx • Py • Dy • Pz • Dz • Pw • Dw) ⊃
• (x≠y • x≠z • x≠w • y≠z • y≠w • z≠w)]

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Definitions:

Conditioned Response

A learned response to a specific stimulus as a result of conditioning.

Trace Conditioning

A form of conditioning in which the conditioned stimulus (CS) and unconditioned stimulus (UCS) are presented separately with a time gap in between, requiring the organism to maintain a memory of the CS to elicit a response.

Delayed Conditioning

A classical conditioning paradigm where the conditioned stimulus is presented and continues until the unconditioned stimulus begins, resulting in learning the association between the two stimuli over time.

Backward Conditioning

A conditioning method where the conditioned stimulus is presented after the unconditioned stimulus, often leading to weaker learning.