Categorical Syllogisms A syllogism is a particular kind of deductive argument containing three categorical claims, two of the claims premises, one a conclusion. Stated another way, on the assumption the premises are true, the conclusion must follow. All dogs are mammals.
All terriers are dogs.
Therefore, all terriers are mammals. To avoid confusion in diagramming syllogisms using Venn diagrams, we will always use the upper left circle to represent the minor term, the upper right circle to represent the major term, and the lower circle to represent the middle term. There is nothing sacred about these choices and you may certainly make your own choices. You diagram the subject of each of the premises . But these areas are already shaded when diagramming the premises, proving that areas 1 and 5 are not empty.