1. Lesson 2.3 p. 87 Deductive Reasoning Goals: to use symbolic notation to apply the laws of logic

2. Symbolic Notation Conditional Statements Hypothesis “p”Conclusion “q” p Example: If today is Monday, then there is school. q

3. Symbolic Notation Conditional Statement: If p, then qorp q Biconditional : If p q and if q p or p q p if and only if q Converse: If q, then porq p If today is Monday, then there is school. If there is school, then today is Monday. Today is Monday, if and only if there is school.

4. More Symbolic Notation

5. Example Converse or q p: Conditional Statement or p q: Tim will buy a car if he finds a summer job. Inverse or Contrapositive or q: p:

6. Deductive Reasoning vs. Inductive Reasoning Inductive Reasoning: Uses previous examples Uses patterns Can make an educated guess Example: Kate lost her instrument. The only instrument Kate plays is the clarinet. Kate lost her clarinet. Deductive Reasoning: Uses facts Uses definitions Can prove or make a logical argument Example: It rained for the last two days, so it will rain today.

7. Two Laws of Deductive Reasoning 2)Law of Syllogism: If p q and q r are true conditional statements, then p r is true. 1) Law of Detachment: If p q is a true conditional statement and p is true, then q is true. Example: Jamal knows that if he misses practice the day before a game, then he will not be able to pitch. Jamal misses practice on Tuesday. Jamal will not be able to pitch in the game on Wednesday. Example: If it is Friday, then tomorrow is Saturday. If it is Saturday, then we will go swimming. If it is Friday, then tomorrow we will go swimming.

8. Examples of Laws of Deductive Reasoning 2)Law of Syllogism: If p q and q r are true condition statements, then p r is true. 1) Law of Detachment: If p q is a true condition statement and p is true, then q is true. Example: If two angles form a linear pair, then they are supplementary. Angles A and B are supplementary. Conclusion, or can it not be reached? Example: If I break my leg, then I can’t ice skate. If I can’t ice skate, I won’t go to the ice skating party. Conclusion:

9. Example A foot is a measurement of twelve inches. If-then form: Converse: Inverse: Contrapositive: