H ⊃ ∼M
A) DA-invalid.
B) MP-valid.
C) AC-invalid.
D) MT-valid.
E) HS-valid.

Question

H ⊃ ∼M 
A) DA-invalid. 
B) MP-valid. 
C) AC-invalid. 
D) MT-valid. 
E) HS-valid.

Quizplus · Accepted Answer

This statement is in the form of a conditional statement. In order to use the method of modus tollens (MT), we need to negate the consequent (M). Therefore, the contrapositive of this statement is M ⊃ ∼H. The statement we are given is the inverse of the contrapositive. However, we can still use the method of modus tollens to arrive at our conclusion. Assume ∼∼M, which is equivalent to M. From the given statement, we know H ⊃ ∼M. Therefore, if ∼M is true, then ¬H must also be true (by modus tollens). Therefore, the argument is valid by modus tollens.