determine whether the given argument is valid or invalid. If it is invalid, select a counterexample.
-1. (∃x)[(Dx • Ex) • Fx]
2) (∀x)[(Dx • Fx) ⊃ ∼Gx] / (∃x)(Ex • ∼Gx)
A) Valid
B) Invalid. Counterexample in a domain of 1 member, in which:
Da: True Ea: True Fa: True Ga: True
C) Invalid. Counterexample in a domain of 1 member, in which:
Da: True Ea: True Fa: True Ga: False
D) Invalid. Counterexample in a domain of 1 member, in which:
Da: True Ea: True Fa: False Ga: True
E) Invalid. Counterexample in a domain of 1 member, in which:
Da: False Ea: True Fa: True Ga: True

Question

Quizplus · Accepted Answer

The argument is valid because the premises logically lead to the conclusion. The first premise states there exists an x such that Dx, Ex, and Fx are all true. The second premise states that for all x, if Dx and Fx are true, then Gx is not true (¬Gx). Given that there exists an x for which Dx, Ex, and Fx are true, it follows from the second premise that for this x, Gx is not true. Therefore, there exists an x for which Ex is true and Gx is not true, which is exactly what the conclusion states.

Determine Whether the Given Argument Is Valid or Invalid