Select a Counterexample for the Given Invalid Argument

question 195

Multiple Choice

select a counterexample for the given invalid argument.
-1. (∃x) Sx
2) (∀x) [Sx ⊃ (Tx ⊃ ∼Ux) ]
3) Ua • Ub
4) (∃x) ∼Ux / (∃x) (Sx • ∼Tx)

• A) Counterexample in a domain of 3 members, in which:
• Sa: True Ta: False Ua: True
• Sb: False Tb: False Ub: True
• Sc: True Tc: True Uc: False
• B) Counterexample in a domain of 3 members, in which:
• Sa: False Ta: False Ua: True
• Sb: True Tb: True Ub: False
• Sc: True Tc: True Uc: False
• C) Counterexample in a domain of 3 members, in which:
• Sa: True Ta: False Ua: True
• Sb: True Tb: True Ub: True
• Sc: True Tc: True Uc: False
• D) Counterexample in a domain of 3 members, in which:
• Sa: False Ta: False Ua: False
• Sb: False Tb: True Ub: False
• Sc: True Tc: True Uc: False
• E) Counterexample in a domain of 3 members, in which:
• Sa: False Ta: False Ua: True
• Sb: False Tb: True Ub: True
• Sc: True Tc: True Uc: False

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Definitions:

Causal Hypothesis

A statement predicting a precise relationship between two or more variables, where changes in one variable cause changes in another.

Initial Causal Hypothesis

The original assumption or proposition about the cause-and-effect relationship between variables, awaiting testing or verification.

Salient Aspect

A feature or characteristic that stands out prominently and is often the focus of attention or consideration.

Kelley's Covariation Model

a psychological theory that explains how individuals attribute cause to behavior based on the consistency, distinctiveness, and consensus of the observed action.