1. Ha • Ia
2. (∀x)[(Hx • Ix) ⊃ x=a]
3. Hb • Jb
4. (∀x)[(Hx • Jx) ⊃ x=b]
5. Ka • ∼Kb
-Which of the following propositions is derivable from the given premises in F?
A) ~(∀x)Hx
B) (∀x)(Kx ⊃ x=a)
C) (∃x)(Ix • Jx)
D) (∀x)(~Kx ⊃ x=b)
E) ∼(∃x)(Hx • Ix • Jx)

Question

Quizplus · Accepted Answer

The premises suggest that for any x, if Hx and Ix are true, then x must be a. Similarly, for any x, if Hx and Jx are true, then x must be b. Since a and b are distinct, there cannot be an x such that Hx, Ix, and Jx are all true simultaneously. Therefore, ∼(∃x)(Hx • Ix • Jx) is derivable.