Solved

Provide a Conterexample in a Finite Domain to Each Given

Question 39

Multiple Choice

provide a conterexample in a finite domain to each given invalid argument.
-1. (∀x) [Px ⊃ (∃y) Qxy]
2) (∀x) [(∃y) Qxy ⊃ (∃y) Rxy]
3) Pa / Rab

A) Counterexample in a domain of two members, in which:
Pa: True Qaa: False Qba: True Raa: True Rba: False
Pb: False Qab: False Qbb: True Rab: False Rbb: True
B) Counterexample in a domain of two members, in which:
Pa: True Qaa: True Qba: False Raa: True Rba: True
Pb: False Qab: True Qbb: False Rab: False Rbb: False
C) Counterexample in a domain of two members, in which:
Pa: True Qaa: False Qba: False Raa: False Rba: True
Pb: True Qab: True Qbb: False Rab: False Rbb: True
D) Counterexample in a domain of two members, in which:
Pa: True Qaa: True Qba: True Raa: True Rba: False
Pb: False Qab: False Qbb: True Rab: True Rbb: True
E) Counterexample in a domain of two members, in which:
Pa: True Qaa: True Qba: True Raa: False Rba: False
Pb: True Qab: False Qbb: False Rab: False Rbb: False

Correct Answer: