Final answer:
Validity of an argument is determined by whether the logical structure of premises necessitates the conclusion. Disjunctive syllogism is relevant for the premise '(N • I) ∨ (G • C)', which should be analyzed along with the other premises to see if the conclusion 'G • M' necessarily follows.
Step-by-step explanation:
When analyzing the given argument using indirect truth tables, we are aiming to determine whether the argument is valid, meaning if the premises are true, the conclusion must necessarily also be true. Validity is determined by the logical form of the premises leading to the conclusion, which should be consistent with valid deductive inferences such as modus ponens, modus tollens, and disjunctive syllogism. Considering the argument's structure, we need to examine whether the premises provided logically necessitate the truth of the conclusion, which is 'G • M'.
Let's look at the last form mentioned which is disjunctive syllogism, this form of reasoning is important for us because of the premise given as '(N • I) ∨ (G • C)'. Disjunctive syllogism follows the pattern:
1. X or Y.
2. Not Y.
3. Therefore X. In this argument, if we consider 'N • I' as Y and 'G • C' as X in the structure of disjunctive syllogism, we can infer that if 'N • I' is false, 'G • C' must be true.
However, the actual work of verifying the validity would involve testing the possible truth values of the given premises and determining whether there's any case in which all premises are true and the conclusion is false. If there is no such case, the argument is valid. If there is a case, the argument is invalid. Upon the detailed analysis considering the logical structures, if we find that the premises, when true, do not guarantee the truth of 'G • M', the argument would be classified as invalid. Conversely, if the truth of 'G • M' is guaranteed, the argument is valid. We should also note that an argument can be valid even if some of its premises are false; validity is not about the actual truth of premises but about the logical connection between premises and conclusion.