Question

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

1. C ⊃ (H ∙ M)
2. (T ⊃ S) ⊃ C
3. T
Select one:
a. S 2, 3, MP
b. (T ⊃ S) ⊃ (H ∙ M) 1,2, HS
c. T ⊃ (S ∙ C) 2, Exp
d. (C ⊃ H) ∙ M 1, Assoc
e. (C ⊃ H) ∙ (C ⊃ M) 1, Dist

Answer 1

The conclusion that follows in a single step from the given premises is S.

Step-by-step explanation:

The conclusion that follows in a single step from the given premises is S. The correct answer is option a. (S 2, 3, MP). In modus ponens, if premise 1 states that X is sufficient for Y and premise 2 states that X is true, then the conclusion (Y) necessarily follows. In this case, premise 2 states that T is true and premise 3 states that T, so the conclusion S follows. Therefore, option a is the correct answer.