provide a conterexample in a finite domain to each given invalid argument.
-1. (∀x)[(∃y)(Fxy • Gy) ⊃ (∀y)(Gy ⊃ Fxy)]
2) Ga / (∀x)(Fxa ⊃ Fax)
A) Counterexample in a domain of two members, in which: Ga: True Faa: True Fba: True
Gb: False Fab: False Fbb: True
B) Counterexample in a domain of two members, in which: Ga: True Faa: False Fba: True
Gb: True Fab: False Fbb: False
C) Counterexample in a domain of two members, in which: Ga: True Faa: True Fba: True
Gb: False Fab: True Fbb: False
D) Counterexample in a domain of two members, in which: Ga: False Faa: True Fba: False
Gb: False Fab: True Fbb: True
E) Counterexample in a domain of two members, in which: Ga: True Faa: False Fba: True
Gb: True Fab: True Fbb: False

Question

Quizplus · Accepted Answer

The counterexample in option A shows that the argument is invalid because the premise (∃y)(Fxy • Gy) is true for x = a and y = b, but the conclusion (∀y)(Gy ⊃ Fxy) is false because Gy is false for y = b and Fby is false.

Provide a Conterexample in a Finite Domain to Each Given