Given the following premises:
1)C ⊃ (H • M)
2)(T ⊃ S) ⊃ C
3)T
A)(C ⊃ H) • M 1, Assoc
B)T ⊃ (S • C) 2, Exp
C)(C ⊃ H) • (C ⊃ M) 1, Dist
D)S 2, 3, MP
E)(T ⊃ S) ⊃ (H • M) 1, 2, HS

Question

Quizplus · Accepted Answer

Using the premises, we can apply the Hypothetical Syllogism (HS) rule to deduce (T ⊃ S) ⊃ (H • M) from premises 1 and 2. Then using Modus Ponens (MP) with premise 3, we can deduce T. Finally, again using HS, we can deduce (H • M) from the two previous conclusions. Therefore, the correct answer is E.

Given the Following Premises