Sec 2-3

1. Sec 2-3 Concept: Deductive ReasoningObjective: Given a statement, use the laws of logic to form conclusions and determine if the statement is true through completion of daily work

2. Example 1: Use the true statements to determine whether the conclusion is true or false. Explain your reasoning • If Diego goes shopping, then he will buy a pretzel • If the mall is open, then Angela and Diego will go shopping • If Angela goes shopping, then she will buy a pizza • The mall is open a. Diego bought a pretzel TRUE! Since the mall is open, Angela and Diego go shopping and therefore, Diego buys a pretzel

3. Example 1 cont.: Use the true statements to determine whether the conclusion is true or false. Explain your reasoning • If Diego goes shopping, then he will buy a pretzel • If the mall is open, then Angela and Diego will go shopping • If Angela goes shopping, then she will buy a pizza • The mall is open b. Angela and Diego went shopping TRUE! Since the mall is open, Angela and Diego went shopping

4. Example 1 cont.: Use the true statements to determine whether the conclusion is true or false. Explain your reasoning • If Diego goes shopping, then he will buy a pretzel • If the mall is open, then Angela and Diego will go shopping • If Angela goes shopping, then she will buy a pizza • The mall is open c. Angela bought a pretzel FALSE! Since the mall is open, Angela and Diego went shopping, therefore, Angela bought a pizza

5. Example 1: Use the true statements to determine whether the conclusion is true or false. Explain your reasoning • If Diego goes shopping, then he will buy a pretzel • If the mall is open, then Angela and Diego will go shopping • If Angela goes shopping, then she will buy a pizza • The mall is open d. Diego had some of Angela’s Pizza FALSE! Since the mall is open, Angela and Diego went shopping, therefore, Diego bought a pretzel

6. A. B. Example 2: Deductive Reasoning

7. 4. ~p→~q 5. q→p 6. ~q→~p Example 3: Write the symbolic statement in words. p: the sky is cloudy q: it is raining 1. ~p The sky is not cloudy 2. ~q It is not raining 3. p→q If the sky is cloudy, then it is raining If the sky is not cloudy, then it is not raining. If it is raining, then the sky is cloudy If it is not raining, then the sky is not cloudy 7. p↔q The sky is cloudy if and only if it is raining.

8. Example 4: Determine if statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. p q • If you are a teenager, then you are always right • If you are always right, then people will listen to you • If you are a teenager, then people will listen to you q r r p Law of Detachment: If p→q is a true conditional statement and p is true, then q is true Law of Syllogism: If p→q and q→r, then p→r LAW OF SYLLOGISM

9. Example 4 Continued: Determine if statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. p q true • If an angle is acute, then it is not obtuse • <ABC is actue • <ABC is not obtuse p: true q: must be true Law of Detachment: If p→q is a true conditional statement and p is true, then q is true Law of Syllogism: If p→q and q→r, then q→r Law of Detachment

10. Today’s Work