Advanced Placement (AP) English Language and Composition Practice Exam

What is an example of the pattern associated with the undistributed middle?

1. All cats are mammals; all dogs are mammals; therefore, all dogs are cats

2. All teachers are professionals; John is a teacher; therefore, John is a professional

3. All birds can fly; all sparrows can fly; therefore, all sparrows are birds

4. No insects are mammals; all beetles are insects; therefore, all beetles are mammals

The correct answer is: All cats are mammals; all dogs are mammals; therefore, all dogs are cats

The example illustrating the pattern associated with the undistributed middle is when it presents a logical fallacy in the form of an incorrect conclusion drawn from two premises that share a common term but do not logically connect the subjects and predicates in a valid way. In the case of the chosen answer, the premises state that all cats are mammals and all dogs are mammals. While it's true that both cats and dogs belong to the broader category of mammals, the conclusion that all dogs are cats is logically flawed. This fallacy occurs because the shared term "mammals" fails to distribute the relationship between the subjects (cats and dogs) adequately, leading to an erroneous conclusion. In contrast, the other options present valid logical structures. The second option correctly uses the relationship that all teachers fall under the category of professionals, allowing for a sound conclusion about John being a professional based on his classification as a teacher. The third option shows that all sparrows can fly, which is true for birds, but it does not incorrectly assert that all sparrows are birds based solely on their ability to fly. Lastly, the fourth option states that all beetles being insects, together with the premise that no insects are mammals, leads to the valid conclusion that beetles are not