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Introducing PL

# Introducing PL - Todays Topics(10/19 I II Introducing...

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3/4/11 Today’s Topics (10/19) I. Introducing Propositional Logic II. One way of Identifying the Form of Propositions III. Propositional Connectives IV. Compound, Component, and Simple Propositions V. A Second Way of Identifying the Form of Propositions

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3/4/11 I. Introducing Propositional Logic Propositional logic is a branch of formal logic. What makes it formal is that it abstracts from the content of propositions to study their form. A form of a proposition (called it’s ‘propositional form’) is a general pattern
3/4/11 And Or Not If…then James is happy and Sarah is sad. Either I will pass the test or I will fail the class. It is not the case that Stacy is at the bar. If you eat bugs, then you are gross. Ducks quack and dogs bark. Either Jason is from Elm Street or Freddy is from Elm Street. James is not in the army. If Freddy is on Elm Street, you don’t want to be there. Obama is the president and Biden is the vice-president. Either Obama will get re- elected or a Republican will get elected. Lady Gaga will not be elected president of the U.S. If Obama is re- elected, Sarah Palin will be sad. Martians visit me at night and goblins visit me in the morning. Either morality is objected or everything is permitted. Kant was unmarried. If I had a hammer, I’d hammer in the morning. What do these propositions have in common?

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II. One Way to Identify a Form Ø In propositional logic, we use lower case letters as variables for propositions. Ø One way of identifying the form of a proposition is to replace the entire proposition with a single Proposition Propositio nal Form James is happy and Sarah is sad. p Ducks quack and dogs bark. p Obama is the president and Biden is the vice- president. p Proposition Propositio nal Form Either I will pass the test or I will fail the class. p Either Jason is from Elm Street or Freddy is. p Either Obama will get re-elected or a Republican will get p
3/4/11 Every conceivable proposition has the propositional form: p But we also want a way of representing the fact And Or James is happy and Sarah is sad. Either I will pass the test or I will fail the class. Ducks quack and dogs bark. Either Jason is from Elm Street or Freddy is.

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Introducing PL - Todays Topics(10/19 I II Introducing...

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