Apologies for the confusion in my previous response. Let me clarify the deductive and inductive reasoning in the given situations.
1. All students are eligible to be in the dean's list. Vincent is a student. Therefore, it can be concluded that Vincent is eligible to be in the dean's list.
This is an example of deductive reasoning because the conclusion follows logically from the given premise. The premise states that all students are eligible for the dean's list, and Vincent is identified as a student, so the conclusion can be drawn with certainty.
2. All dogs are mammals, and all humans are vertebrates. Trisha is a dog. From this information, we can deduce that Trisha is a mammal. However, we cannot deduce anything about whether Trisha is a vertebrate, as being a dog does not necessarily imply that Trisha is a human.
This situation involves both deductive and inductive reasoning. The premise that all dogs are mammals is a deductive statement because it is a generalization that applies to all dogs. Therefore, we can deduce that Trisha, being a dog, is a mammal. However, the premise that all humans are vertebrates is also a generalization, but it does not specifically apply to Trisha, who is a dog. Therefore, we cannot deduce that Trisha is necessarily a vertebrate. Instead, we would need further information or evidence to draw a conclusion about Trisha's classification as a vertebrate or non-vertebrate.