determine whether the given argument is valid or invalid. If it is invalid, select a counterexample.
-1. (∀x)[Fx ⊃ (Gx $ \lor $ Hx)]
2) (∀x)(Gx ⊃ ∼Ix)
3) ∼(∃x)(Hx • Ix)
4) Fg / ∼Ig
A) Valid
B) Invalid. Counterexample in a domain of 1 member, in which: Fg: True Gg: True Hg: True Ig: True
C) Invalid. Counterexample in a domain of 1 member, in which: Fg: True Gg: False Hg: True Ig: True
D) Invalid. Counterexample in a domain of 1 member, in which: Fg: True Gg: False Hg: False Ig: True
E) Invalid. Counterexample in a domain of 1 member, in which: Fg: True Gg: True Hg: False Ig: True

Question

Quizplus · Accepted Answer

The argument is valid because if Fg is true, then Gg or Hg must be true (from 1). If Gg is true, then Ig must be false (from 2), satisfying the conclusion. If Hg is true, given that there cannot exist an x such that both Hx and Ix are true (from 3), and since Fg implies Gg or Hg, the conclusion ∼Ig follows logically.

Determine Whether the Given Argument Is Valid or Invalid ∨ \lor ∨

Determine Whether the Given Argument Is Valid or Invalid $\lor$