Final answer:
The statement ~MM ⊃ ~G is a conditional statement, and only Modus Tollens (MT) is a valid form of inference for the argument 'Ga', indicating option 'b' as valid. Other forms of inference like Affirming the Consequent (AC), Disjunctive Syllogism (DS), Denying the Antecedent (DA), and Modus Ponens (MP) do not yield a valid argument from the given statement, marking them as invalid.
Step-by-step explanation:
The question asks us to determine the validity of certain deductive argument forms based on a given conditional statement, which is task that falls under the subject of logic, a subset of philosophy. Specifically, the conditional statement provided is '¬MM ⊃ ¬G' and we are asked to evaluate whether the argument 'Ga' can be validly inferred from the initial statement using different rules of inference such as Affirming the Consequent (AC), Modus Tollens (MT), Disjunctive Syllogism (DS), and Denying the Antecedent (DA), as well as Modus Ponens (MP).
Analysis of the Options:
- b. MT—valid: This is a correct application of Modus Tollens because if the statement is 'If not MM, then not G', then affirming G (contrapositive) allows us to deny MM, which would make the argument valid.
- e. MP—valid: This is incorrect. Modus Ponens requires affirming the antecedent to infer the consequent; however, the antecedent in this case (¬MM) is not affirmed.
- a. AC—invalid, c. DS—invalid, and d. DA—invalid: These options are stating invalid forms because they do not adhere to the proper application of valid deductive reasoning based on the provided statement.