determine whether the given argument is valid or invalid. If it is invalid, select a counterexample.
-1. (∃x)(Jx • ∼Kx) ⊃ (∃x)(Lx • Mx)
2) (∃x)(Jx • Lx)
3) ∼(∃x)(Jx • Kx) / ∼(∀x)(Lx ⊃ Mx)
A) Valid
B) Invalid. Counterexample in a domain of 1 member, in which:
Ja: True Ka: False La: True Ma: True
C) Invalid. Counterexample in a domain of 1 member, in which:
Ja: False Ka: False La: True Ma: True
D) Invalid. Counterexample in a domain of 1 member, in which:
Ja: True Ka: True La: True Ma: True
E) Invalid. Counterexample in a domain of 1 member, in which:
Ja: True Ka: False La: False Ma: False

Question

Quizplus · Accepted Answer

Assuming a domain of 1 member where Ja is true, Ka is false, La is true, and Ma is false, the premise (∃x)(Jx • ∼Kx) is true because there exists an x (in this case, the only member in the domain) that satisfies both Jx and ∼Kx. However, the conclusion (∃x)(Lx • Mx) is false because no x in the domain satisfies both Lx and Mx. Therefore, the argument is invalid and the correct answer is B.

Determine Whether the Given Argument Is Valid or Invalid