2 6 Using Euler Diagrams to Verify Syllogisms

2. 6 Using Euler Diagrams to Verify Syllogisms l Use Euler diagrams to identify a valid syllogism. l Use an Euler diagram to identify an invalid syllogism.

Syllogisms – consist of a set of statements called premises followed by a statement called a conclusion and may contain quantifiers such as all, some, and none. l A syllogism is valid if whenever its premises are all true, then the conclusion is also true. l A syllogism is invalid when the conclusion is false even though all the premises are true. l

Euler Diagrams l Euler diagram – a diagram that can be used to determine whether a syllogism is valid.

Valid Syllogism All poets are good spellers. Dante is not a good speller. Dante is not a poet. Dante poets Good spellers

Invalid Syllogism All tigers are meat eaters. Simba is a meat eater. Simba is a tiger. Meat eaters Tigers Simba

The Counterexample Principle l In testing the validity of a syllogism, it is a good strategy to draw several diagrams, with the idea that one of them may show the syllogism to be invalid. If you are convinced that no diagram can show the syllogism to be invalid, then you can conclude that the syllogism is valid.

Classwork/Homework • Classwork – Page 128 (9 – 19 odd, 31) • Homework – Page 128 (10 – 20 even, 32)