Question

True/False Review and Chapter SummaryUse your knowledge of argument forms and the counterexample method to determine which, if any, of the following statements are true.Check all that apply.Every argument form is either a valid form or an invalid form.Counterexamples are used to prove the validity of an argument.When attempting to give a counterexample, you should substitute terms or statements that will yield premises and a conclusion with indisputable truth values.In an argument form for a hypothetical syllogism, the letters will stand for statements.A substitution instance with true premises and a true conclusion will not prove that an argument form is valid.A counterexample may have false premises and a false conclusion.A substitution instance is a representation of the logical structure of an argument using form words and letters.To represent the logical relationships in an argument, an argument form uses capital letters as a replacement for the meaningful content.Any set of sentences such that some are true and another is false is a counterexample to every invalid argument form.Not all valid arguments have the same argument form.Some valid arguments are substitution instances of invalid argument forms.If an argument is a substitution instance of both a valid argument form and an invalid argument form, then the argument is valid.Since it is impossible for the premises to be true and the conclusion to be false when an argument is valid, it follows that no counterexample can be given to a valid argument form.It is possible to give a counterexample to a valid argument that has false premises and a false conclusion.Some invalid arguments have valid argument forms.

Answer 1

Every argument form is either a valid form or an invalid form. A substitution instance is a representation of the logical structure of an argument using form words and letters. If an argument is a substitution instance of both a valid argument form and an invalid argument form, then the argument is valid.

Step-by-step explanation:

The statements that are true are:

1. Every argument form is either a valid form or an invalid form.
2. A substitution instance is a representation of the logical structure of an argument using form words and letters.
3. If an argument is a substitution instance of both a valid argument form and an invalid argument form, then the argument is valid.

The statements that are false are:

1. Counterexamples are used to prove the validity of an argument.
2. In an argument form for a hypothetical syllogism, the letters will stand for statements.
3. A substitution instance with true premises and a true conclusion will not prove that an argument form is valid.
4. A counterexample may have false premises and a false conclusion.
5. To represent the logical relationships in an argument, an argument form uses capital letters as a replacement for the meaningful content.
6. Any set of sentences such that some are true and another is false is a counterexample to every invalid argument form.
7. Not all valid arguments have the same argument form.
8. Some valid arguments are substitution instances of invalid argument forms.
9. Since it is impossible for the premises to be true and the conclusion to be false when an argument is valid, it follows that no counterexample can be given to a valid argument form.
10. It is possible to give a counterexample to a valid argument that has false premises and a false conclusion.
11. Some invalid arguments have valid argument forms.