1. ∼(∃x)[Fx • (Gx • Hx)]
2. ∼(∃x)(Ix • ∼Fx)
-Which of the following propositions is derivable from the given premises in M?
A) (∀x)(∼Gx $ \lor $ ∼Hx)
B) (∀x)[(Ix $ \lor $ (∼Gx • ∼Hx)]
C) (∀x)[Ix ⊃ (∼Gx $ \lor $ ∼Hx)]
D) (∃x)(∼Gx $ \lor $ ∼Hx)
E) (∃x)Fx

Question

Quizplus · Accepted Answer

To derive proposition C, we can use universal instantiation to obtain (∼Gy • ∼Hy) for any object y, and then use modus ponens with proposition 2 to obtain Iy, and finally use conditional introduction to obtain the desired result for any object y. Therefore, (∀x)[Ix ⊃ (∼Gx $ \lor $ ∼Hx)] is derivable from the given premises. None of the other answer choices can be derived from the premises.

1 ∼(∃X)[Fx • (Gx • Hx)] 2 ∨ \lor ∨ ∼Hx) B) (∀X)[(Ix

1 ∼(∃X)[Fx • (Gx • Hx)]
2 $\lor$ ∼Hx)
B) (∀X)[(Ix