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

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

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.

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

Valid Syllogisms Example (solution on next slide)

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.

Invalid Syllogisms Example: Solution:

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

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

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

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

Invalid Syllogisms Example: (solution on next slide)

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

Invalid Syllogisms

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

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

Implicit Conditions in Euler Diagrams Solution: