Question

Select the conclusion that follows in a single step from the given premises.

1. G • ~A
2. K ⊃ (G • ~A)
3. G ⊃M
Group of answer choices
A. (K ⊃ G ) ⊃ ~A 2, Exp
B. K ⊃ (~A • G) 2, Com
C. (K ⊃ G) • ~A 2, Assoc
D. K 1, 2, MP
E. M 1, 3, MP

Answer 1

The correct conclusion drawn in a single step from the given premises is option B, which utilizes modus ponens and the commutation of conjunction to assert that K implies both ~A and G.

Step-by-step explanation:

The question is asking to identify which conclusion follows from the given premises using a single logical step. We have the premises:

1. G • ~A
2. K ⊕ (G • ~A)
3. G ⊕ M

Examining the premises and options given, the correct conclusion that can be drawn in a single step is that if premise 1 (G • ~A) is true and there's a premise stating K implies (G • ~A), which is premise 2 (K ⊕ (G • ~A)), then we can infer that if K is true, G must be true, which is a requisite for conjecturing that ~A is also true. Therefore, option B correctly states that K implies both ~A and G, taking into account the commutation of the conjunction in premise 2. This is the only option that directly follows from a single step from the given premises, making use of modus ponens.