More on Deductive Arguments All arguments on the Worksheet are Deductive. Follow the directions in each section. A. Exercise with Conditional/Hypothetical Arguments (20 points) Put the following...

More on Deductive Arguments

All arguments on the Worksheet are Deductive. Follow the directions in each section.

A. Exercise with Conditional/Hypothetical Arguments (20 points)

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  Put the following arguments into standard form.
  
  

  
  


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  UsingHow to Identify Hypothetical Argument Forms, which was in last week's material, identify each as modus ponens, modus tollens, chain argument, denying the antecedent or affirming the consequent.
  
  

  
  


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  Indicate whether the argument form is valid or invalid, in terms of the logic.
  
  

  
  

1. If we are in Sydney, we are in Australia. We are not in Australia. So we are not in Sydney.
   
   


2. If we are in Calgary, we are in Canada. We are in Canada. So we are in Calgary.


3. If we’re in Oregon, we’re in North America. We are in Oregon. So, we’re in North America.


4. If we are in Shanghai, then we are in China. If we are in China, then we are in Asia. So, if we are in Shanghai, then we are in Asia.


5. If we are in Seattle, then we are in the United States. We are not in Seattle. So, we are not in the United States.


6. If we are in Berlin, then we are in Germany. So, we are in Germany, because we are in Berlin.


7. We are not in Kenya because if we are in Nairobi, we are in Kenya, and we are not in Nairobi.


8. Since we’re in Egypt, we are in Cairo, since we are in Egypt if we are in Cairo.


9. If we’re in Rio de Janeiro, then we are in Brazil. So, because if we are in Brazil, we are in South America, if we are in Rio de Janeiro, we are in South America.


10. We’re in Amman, given that if we are in Amman, we are in Jordan, and we are in Jordan.

B. Identifying valid deductive arguments: determine whether or not the arguments below are valid. (10 points)

Remember that to be valid, the premises must necessarily lead to the conclusion.

1. It is totally dark in here, but I know that this drawer has socks in it: blue socks and brown socks. There 10 of each color, so I need to grab 11 socks to be sure I have a pair that matches.


2. 
   Molly: I'm going to bring my phone to the logic exam tomorrow. If I get stuck on an answer, I'll text my roommate.Emma:Are you nuts? Dr. Chi won't let you cheat like that.Molly: Shewill. I heard her say "No study materials in any form are allowed during the exam," and texts are not study material. Think about it logically: No study materials are allowed during the exam; text messages aren't study materials, so they're OK.Emma: You are definitely going to need help on this exam!


3. 
   Student:Science is often defined as 'the organized arrangement of known facts'. But that cannot be the correct definition, because an encyclopedia is an organized arrangement of facts, and an encyclopedia is NOT science.
   
   


4. Silver is a horse. Necessarily, then, Silver must have four hooves.


5. If King Kong is human, then King Kong must have blood. King Kong is not human, so King Kong doesn't have any blood.


6. If anything is a robin, then it is a bird. A bat is not a bird. Therefore, a bat isn't a robin.
   
   


7. If we are on Mars, then we are not on earth. We are not on Mars, so we are on earth.


8. Some people like hamburgers. Some people like cheese. It follows that there must be some people who like both hamburgers and cheese.
   
   


9. Your mother can't be a logger. Only men are loggers, and your mother is not man.
   
   


10. I guess some of the cross-country team was late to practice yesterday. I heard Coach say that anyone late to practice yesterday would have to do push-ups, and I saw some of the cross-country team doing push-ups.

C. Recognizing sound deductive arguments (20 points):

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  Decide whether each argument is sound, that is, uses good logic (is valid), and has true premises.
  
  

  
  


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  If the argument is not sound, indicate why--is it the logic, the premises, or both?
  
  

  
  

1. Valentine's Day is always on a Saturday. So the day after Valentine's Day is always on a Sunday.


2. Some grapes are green. Some grapes are sweet. So, some grapes are green and sweet.
   
   


3. India has a larger population than Brazil. Brazil has a larger population than Liechtenstein. So, India must have a larger population than Liechtenstein.


4. If Warren Buffett is a billionare, then he's wealthy. Warren Buffett is wealthy, so he's a billionaire.


5. Either elephants are lions or elephants are tigers. Elephants are not lions. So, elephants, then, are tigers.


6. All cockroaches are insects. All insects are animals. So, all cockroaches are animals.


7. If John Kerry plays for the Portland Train Blazers, then he is a professional basketball player. John Kerry does not play for the Blazers, so John Kerry isn't a professional basketball player.


8. If Oaxaca is in Mexico, then Oaxaca is in North America. Oaxaca is in Mexico. Therefore, Oaxaca is in North America.


9. No airplanes are spaceships. The Boeing 757 is an airplane. So, the 757 isn't a spaceship.


10. Seattle is west of Minneapolis. Therefore, Boston is east of Minneapolis, because Boston is east of Seattle.