Determining Semantic Properties with a Model Universe

Solution 3

Test the following arguments for validity:

(x)(Fx ⊃ Gx), (∃x)Fx, ///(x)Gx

Since there are two distinct propositional functions, Fx and Gx, our maximum domain will be a domain of 4. It should be clear that the argument is valid in a domain of one. If that's not clear, check it out.

domain: {a,b}

(Fa ⊃ Ga) & (Fb ⊃ Gb)
Fa v Fb                       
Ga & Gb

So is there a row of the truth table for this instantiation where the premises are true and the conclusion false?

Ga is T
Fa is T
Gb is F
Fb is F

So the argument is invalid in a domain of 2, and so invalid.