select a counterexample for the given invalid argument.
-1. (∀x)(Hx ⊃ ∼Ix)
2) (∀x)(Ix ⊃ Ux) / (∀x)(Hx ⊃ ∼Ux)
A) Counterexample in a domain of 1 member, in which: Ha: True Ia: False Ua: True
B) Counterexample in a domain of 1 member, in which: Ha: False Ia: False Ua: True
C) Counterexample in a domain of 1 member, in which: Ha: True Ia: False Ua: False
D) Counterexample in a domain of 1 member, in which: Ha: False Ia: False Ua: False
E) Counterexample in a domain of 1 member, in which: Ha: False Ia: True Ua: False

Question

Quizplus · Accepted Answer

In choice A, Ha being true and Ia being false does not violate the first premise. Since Ia is false, the second premise (Ix ⊃ Ux) is not applicable, making Ua true not contradict the conclusion (∀x)(Hx ⊃ ∼Ux). This shows the argument's invalidity because it does not necessarily follow that if Hx then not Ux.

Select a Counterexample for the Given Invalid Argument