1. LOGIC CHAPTER 3 1

2. EULER DIAGRAMS: A PROBLEM-SOLVING TOOL 3.5 2

3. All men are mortal. Socrates is a man.  Socrates is mortal. ARGUMENTS 3 premises conclusion An argument is a set of statements, the premises, and a claim that another statement, the conclusion, follows from the premises.

4. EULER DIAGRAMS 4 Q P Basic types of statements in Euler diagrams. All P’s are Q’s.

5. EULER DIAGRAMS 5 Q P No P’s are Q’s.

6. EULER DIAGRAMS 6 Q P Some P’s are not Q’s.

7. EULER DIAGRAMS 7 Q P Some P’s are Q’s.

8. DRAWING EULER DIAGRAMS All men are mortal. Socrates is a man. Socrates is mortal. 8 Mortals Men s

9. VALIDITY OF AN ARGUMENT An argument is valid if the conclusion is true whenever the premises are assumed to be true. If an argument is not valid, it is said to be invalid. 9

10. All professors are wise. Ms. Brown is a professor. Ms. Brown is wise. DRAWING EULER DIAGRAMS 10 W P B VALID

11. DRAWING EULER DIAGRAMS 11 H J D INVALID J ? No drinkers are healthy. No joggers drink.. No joggers are healthy.

12. DRAWING EULER DIAGRAMS 12 W P M INVALID P ? No mathematics teacher is wealthy. No panthers teach mathematics.. No panthers are wealthy.

13. DRAWING EULER DIAGRAMS 13 L A H VALID All hippies have long hair. Some athletes are hippies. Some athletes have long hair.

14. DRAWING EULER DIAGRAMS 14 N M F INVALID F ? Some Nissan owners save money. Some fast drivers save money.. Some fast drivers are Nissan owners.

15. STEPS IN DRAWING EULER DIAGRAMS TO DETERMINE VALIDITY OF ARGUMENTS Step 1. Make an Euler diagram for the first premise. Step 2. Make an Euler diagram for the second premise on top of the one for the first premise. Step 3. The argument is valid if and only if every possible diagram illustrates the argument’s conclusion.

16. DRAWING EULER DIAGRAMS 16 PP F E Englishmen are not Frenchmen. Use Euler diagrams to determine which conclusion can be deduced. No Frenchmen like plum pudding.. a.Some Frenchmen like plum pudding b. Englishmen are not Frenchmen. All Englishmen like plum pudding

17. DRAWING EULER DIAGRAMS 17 WU P No conclusion. P No wasps are unfriendly. No puppies are unfriendly. Use Euler diagrams to determine which conclusion can be deduced. a.No puppies are wasps. b. All wasps are not puppies.

18. DRAWING EULER DIAGRAMS 18 MD A Some math problems need attention. x Some math problems are difficult. All difficult problems need attention. Use Euler diagrams to determine which conclusion can be deduced. a.Some math problems need attention. b. Some math problems are not difficult. END