The Language of Argument

9 5

so m e st a n d a r d s f o r ev a l u a t i n g A r g u m e n t s

11. If George lives in Crawford, then George lives in Texas. If George lives
    in Texas, then George lives in the United States. Hence, if George lives in
    Crawford, he lives in the United States.


12. There can’t be a largest six-digit number, because six-digit numbers are
    numbers, and there is no largest number.

Assume that the following sentences are either true (T) or false (F) as indicated.

All my children are teenagers. (T)

All teenagers are students. (T)

All teenagers are my children. (F)

All my children are students. (T)

Using these assigned values, label each of the following arguments as (a)

either valid or invalid, and (b) either sound or unsound.

1. All my children are teenagers.
   All teenagers are students.
   ∴ All my children are students.


2. All my children are students.
   All teenagers are students.
   ∴ All my children are teenagers.


3. All teenagers are my children.
   All my children are students.
   ∴ All teenagers are students.


4. All teenagers are students.
   All my children are students.
   ∴ All my children are students.

exercise vi

exercise vii

Indicate whether each of the following sentences is true. For those that are

true, explain why they are true. For those that are false, show why they are

false by giving a counterexample.

1. Every argument with a false conclusion is invalid.


2. Every argument with a false premise is invalid.


3. Every argument with a false premise and a false conclusion is invalid.


4. Every argument with a false premise and a true conclusion is invalid.
   (continued)

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