1. Laws of Logic

2. Deductive Reasoning Uses the following to form logical arguments. Facts Example: All humans breath air. Definitions Example: Two lines that do not intersect are parallel. Accepted properties Example: Laws of logic Today we will look at the “laws of logic” that help us form logical conclusions.

3. Law of Detachment If p  q is a true conditional statement and p is true, then q is true. Symbolic:p  q p qq  reads “therefore”

4. Example: p q If I study for the test, then I will pass. p I studied for the test.  q I passed the test.

5. You Try: If you brush your teeth, then you won’t have cavities. Emma brushed her teeth.  Emma won’t have cavities.

6. Law of Syllogism If p  q and q  r are true conditional statements, then p  r is true. Symbols: p  q q  r p  rp  r

7. Example: p  q If I pass the driving test, then I can get a car. q  r If I get a car, then I can get a job.  p  r If I pass the driving test, then I can get a job.

8. You Try: If I go to Florida, then I will go to Orlando. If I go to Orlando, then I will go to Disneyworld. If I go to Florida, then I will go to Disneyworld. Therefore…

9. Determine if a conclusion can be made. If possible, write the conclusion. If not possible, write “INVALID” and explain why. 1. If you live in Loudoun, then you live in Virginia. If you live in Virginia, then you live in the United States. Conclusion: 2. All dairy products contain calcium. Milk is a dairy product. Conclusion: 3. If a mammal is a fish, then it swims. Joe swims. Conclusion: