Syllogisms

Syllogism: Kind of logical argument in which one proposition is assumed because of two premises of a certain form. It is composed of a conclusion and two premises, quantifiers (such as ‘all’, or ‘some’ or ‘no’ and three terms, each of which occurs twice. Example:

All dogs are mammals.
Fido is a dog.
Therefore Fido is a mammal.

Terms in this syllogism: ‘Dogs’, ’Fido’ and ‘Mammals’
Premises: ‘All dogs are mammals’ and ‘Fido is a dog’
Conclusion: ‘Therefore Fido is a mammal’
Quantifier: ‘All’

Venn diagrams

To decide if a syllogism is valid or not, we can draw a "Venn diagram". To represent the syllogism above we draw a big circle with the word "Mammals" and inside of it another one and we label it "Dogs":


As you see in the picture, the circle labeled "Dogs" falls inside of the other one labeled "Mammals", and since Fido is a dog, he is in the "Dogs" group so is correct to say that he is a mammal.