The following statement is an example of ________ reasoning."Only gold members can order pie at the cafeteria, and Joe has pie, so Joe must be a gold member."

The statement is an example of deductive reasoning.

Here's the step-by-step breakdown:

1. The first premise is "Only gold members can order pie at the cafeteria". This is a general rule or principle.

2. The second premise is "Joe has pie". This is a specific observation or fact.

3. The conclusion is "Joe must be a gold member". This is a specific conclusion drawn from the combination of the general rule and the specific observation.

In deductive reasoning, if the premises are true, then the conclusion must also be true. It's a top-down logic used when you have a general principle that you use to predict specific results. In this case, the general principle is that only gold members can order pie, and the specific result is that Joe, who has pie, must be a gold member.