Question

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

Given the following premises:
1. A
2. (A⊃∼T)⊃∼G
3. Q ⊃ (A ⊃∼T)
a. Q⊃(T⊃∼A) 3, Trans
b. (Q⊃A)⊃∼T 3, Assoc
c. A⊃(∼T •∼G) 2, Exp
d. ∼T 1, 3, MP
e. Q⊃∼G 2, 3, HS

Answer 1

The conclusion that follows in a single step from the given premises is Q⊃∼G (option e).

Step-by-step explanation:

The conclusion that follows in a single step from the given premises is Q⊃∼G (option e).

To reach this conclusion, we need to use Modus Ponens, which is a valid deductive inference.

Here's how we can derive the conclusion:

1. From premise 1 and 2, we can use Modus Ponens to derive ∼T.
2. From premise 3, we can use Modus Ponens to derive Q⊃∼T.
3. Using Transitivity, we can combine the derived statements from step 1 and step 2 to arrive at Q⊃∼G.