1. 3
Logic
The Study of What’s True or False or Somewhere in Between

2. Using Euler Diagrams to Verify Syllogisms
3.5
Using Euler Diagrams to Verify Syllogisms
Use Euler diagrams to identify a valid syllogism
Use an Euler diagram to identify an invalid syllogism

3. Valid Syllogisms
A syllogism consists of a set of statements called premises followed by a statement called a conclusion.
A syllogism is valid if whenever its premises are all true, then the conclusion is true.
If the conclusion can be false even though all the premises are true, then the syllogism is invalid.

4. Valid Syllogisms
We can use Euler diagrams to determine the validity of a syllogism.
Syllogism Euler Diagram

5. Valid Syllogisms
Example
(solution on next slide)

6. Valid Syllogisms Solution
If Dante is not a good speller, then he cannot be a poet. The conclusion is valid.
Remember: An argument can be valid even if the premises or the conclusion is false.

7. Invalid Syllogisms
Example:
Solution:

8. Invalid Syllogisms Example: Solution:
The argument is invalid. The premises do not force the conclusion to hold.

9. Invalid Syllogisms
The quantifier some can be misleading in syllogisms. All of these represent the premise “some A’s are B’s”.

10. Invalid Syllogisms
The quantifier some can be misleading in syllogisms. All of these represent the premise “some A’s are B’s”.

11. Invalid Syllogisms
The quantifier some can be misleading in syllogisms. All of these represent the premise “some A’s are B’s”.

12. Invalid Syllogisms
Example:
(solution on next slide)

13. Invalid Syllogisms Solution: Possible Euler diagrams:
The conclusion does not follow from the premises. The syllogism is invalid.

14. Invalid Syllogisms

15. Implicit Conditions in Euler Diagrams
Extra conditions are always present in Euler diagrams.
(example on next slide)

16. Implicit Conditions in Euler Diagrams
Example:
(solution on next slide)

17. Implicit Conditions in Euler Diagrams
Solution: