Logic

1. Logic The Lost Art of Argument

2. Logic - Review Proposition – A statement that is either true or false (but not both) Conjunction – And Disjunction – Or Negation – Not Truth Tables can be used to determine Equivalence Equivalence – Two propositions have the same truth values

3. Conditional Sentences Definition: Conditional Sentence – Given two propositions P, Q. P  Q P implies Q If P, then Q Examples: If it is raining, then the roof is wet. If I am late for class, then it is Monday. If you don’t wear your lucky shirt, then you will lose the game. If 4 is an even number, then 4 > 8 If the moon is round, then the chair is blue

4. Conditional Sentences Definition: Antecedent – If P  Q, then P is called the antecedent. Definition: Consequent – If P  Q, then Q is called the consequent. Identify the Antecedent and Consequent in the following: If it is raining, then the roof is wet. If I am late for class, then it is Monday.

5. Conditional Sentences Definition: Negation – For propositions P and Q, the negation of P  Q is ~P  ~Q Examples: If it is raining, then the roof is wet. Negation: If it is not raining, then the roof is not wet. If I am late for class, then it is Monday. Negation: If I am not late for class, then it is not Monday.

6. Conditional Sentences Definition: Converse – For propositions P and Q, the converse of P  Q is Q  P Examples: If it is raining, then the roof is wet. Converse: If the roof is wet, then it is raining. If I am late for class, then it is Monday. Converse: If it is Monday, then I am late for class.

7. Conditional Sentences Definition: Contrapositive – For propositions P and Q, the contrapositive of P  Q is (~Q)  (~P) Examples: If it is raining, then the roof is wet. Contrapositive: If the roof is not wet, then it is not raining. If I am late for class, then it is Monday. Contrapositive: If it is not Monday, then I am not late for class.

8. Conditional Sentences Transitive Property of Conditional Sentences: P  Q, Q  R, then P  R Examples: If it is raining, then I am late for class. If I am late for class, then it is Monday. If it is raining, then it is Monday.

10. Logic - Review Definition: Conditional Sentence – Given two propositions P, Q. P  Q P implies Q If P, then Q Definition: Antecedent – If P  Q, then P is called the antecedent. Definition: Consequent – If P  Q, then Q is called the consequent. Definition: Negation – For propositions P and Q, the negation of P  Q is ~P  ~Q Definition: Converse – For propositions P and Q, the converse of P  Q is Q  P Definition: Contrapositive – For propositions P and Q, the contrapositive of P  Q is (~Q)  (~P)

11. Logic – Next Time Syllogisms All the old articles in this cupboard are cracked All jugs in this cupboard are old Nothing in this cupboard that is cracked will hold water