Question

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Explanation:

Analyze the relationship between the truth table column and argument validity

An argument is valid if and only if its corresponding conditional statement (the conjunction of the premises implying the conclusion) is a tautology. A tautology is represented by a truth table column containing only true values (\(\text{T}\)).

Evaluate the options for the truth table column and validity

If the argument is valid, the last column of the truth table must consist entirely of true values: \(\text{TTTTTTTT}\). If the argument is invalid, the column must contain at least one false value (\(\text{F}\)), such as \(\text{TTTTFTTT}\) or \(\text{TTFTTTTF}\).

Looking at the options:

• For part (b), the third option is \(\text{TTTTTTTT}\) (all true).
• For part (c), the options are "invalid" and "valid".

Since a valid argument corresponds to a tautology (\(\text{TTTTTTTT}\)), these two choices are logically paired. Standard symbolic arguments evaluated in such homework exercises are typically tested for validity, and a tautology column directly indicates a "valid" argument.

Answer:

Question b

• TTTTFTTT
• TTFTTTTF
• TTTTTTTT (Correct answer)

Question c

• invalid
• valid (Correct answer)