Question

Use standard forms of valid and invalid arguments to determine the validity of the arguments. State which standard form(s) you used to determine your conclusion.

(i) ∼x→y Circle one: Valid or invalid x Standard form(s) used:__________
(ii) a→−b Circle one: Valid or Invalid ∼b→c Standard form(s) used:__________

Answer 1

Argument (i) is invalid as it does not match any standard valid argument forms. Argument (ii) cannot be determined as valid or invalid with the given information because it lacks a complete logical structure.

Step-by-step explanation:

Logical forms can be used to assess the validity of arguments. The validity of an argument is based on its structure or form, not the actual truth value of its premises.

For the first argument (i):

• ¬x → y
• x

This argument does not conform to any standard valid forms such as modus ponens, modus tollens, or disjunctive syllogism, and thus cannot be deemed valid based on the information provided. The presence of premises that do not lead to a conclusive argument establishes the argument as invalid. The standard form used to reach this conclusion is modus tollens, which typically follows the form:

1. P → Q
2. ¬Q
3. Therefore, ¬P

However, this structure doesn't apply to the argument given.

For the second argument (ii):

• a → ¬b
• ¬b → c

This argument also doesn't match the structure of a valid deductive inference such as disjunctive syllogism. Without additional premises or information, we cannot determine if this argument is valid. Valid logical forms would require a connecting premise to determine the conclusion's validity. Thus, this argument remains undetermined with the given information.