Final answer:
The provided reference argument is invalid because it contains a logical fallacy, assuming that qualities of some members of a group (some sweet foods being low fat) apply to all members of a subgroup (all desserts). A counterexample, such as buttercream cake, confirms the fallacy as it is a dessert that is not low fat.
Step-by-step explanation:
The question, "T or F we offer a gluten free dessert," is unrelated to the provided reference argument, which pertains to the validity of a logical argument concerning desserts and their fat content. To address the reference argument:
Assessing the Validity of the Argument
The argument provided goes as follows:
- All desserts are sweet foods.
- Some sweet foods are low fat.
- So all desserts are low fat.
This argument is invalid as it commits a logical fallacy. The fact that some sweet foods are low fat does not imply that all desserts, which are a subset of sweet foods, are also low fat. The counterexample provided exemplifies this with buttercream cake, which is both a dessert and sweet but is not low in fat. This serves to illustrate that the conclusion does not logically follow from the premises.