Exercise 1 Page 46

Let's highlight the common parts between the premises and the conclusion. Premises All $ mammals$ are $ warm-blooded$ All dogs are $ mammals$ Conclusion Therefore, all dogs are $ warm-blooded$ We can see that the conclusion is correct because we are told all dogs are mammals and all mammals are warm-blooded. Then, necessarily that must mean that all dogs are warm-blooded, because they fall in the category of mammal.

Alternative Solution

Alternative Solution

From the given premises, we could think about three sets: warm-blooded, mammals, and dogs. Additionally, the premises give us some relations between these sets.

From the diagram above, we see that the set of all dogs is contained in the set of all the mammals, which is included in the set of all the warm-blooded. Then, all dogs are warm-blooded. Thus, the conclusion is correct.