Arguments: Validity and Logic

Which of the following arguments is valid?

A. Joe is not a plumber. Therefore, it is not true that Joe is a non-plumber.
B. Either Joe is a plumber or Bob is a builder. Joe is not a plumber. Therefore, Bob is not a builder.
C. It is not true that Joe is a plumber. Therefore, Joe is a non-plumber.

The argument that is valid among the given options is:
"Either Joe is a plumber or Bob is a builder. Joe is not a plumber. Therefore, Bob is not a builder."

This argument is valid because it follows the logical structure of a disjunctive syllogism, which states that if there are two options and one option is false, then the other option must be true. In this case, the two options are "Joe is a plumber" and "Bob is a builder." The premise states that Joe is not a plumber, which means that the option "Joe is a plumber" is false. Therefore, according to the disjunctive syllogism, the conclusion can be drawn that the other option, "Bob is a builder," must be true.

The other two arguments are not valid. The first argument, "Joe is not a plumber. Therefore, it is not true that Joe is a non-plumber," contains a contradiction because if Joe is not a plumber, then he is indeed a non-plumber.

The second argument, "It is not true that Joe is a plumber. Therefore, Joe is a non-plumber," is invalid because it makes an unsupported inference. The fact that it is not true that Joe is a plumber does not automatically lead to the conclusion that he is a non-plumber. It leaves open the possibility that Joe may have a different occupation altogether.