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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 6

  1. Determine whether each argument is valid or invalid. If invalid, determine the error in reasoning.
    1. If I inherit $1000, I will buy you a cookie. I inherit $1000. Therefore, I will buy you a cookie.

    2. All cats are animals. This is not an animal. Therefore, this is not a cat.

  2. Determine whether each argument is valid or invalid. If invalid, determine the error in reasoning.
    1. If Alice drinks the bottle marked "poison," then she will become sick. Alice does not drink from a bottle that is marked "poison." Therefore, she does not become sick.

    2. If Ron uses Motor oil, then his car is in good condition. Ron's car is in good condition. Therefore, Ron uses Motor oil.

     

  3. Form a valid conclusion from the following statements.
    1. If I am tired, then I cannot finish my homework. If I understand the material, then I can finish my homework.

    2. Everyone who is sane can do logic. No lunatics are fit to serve on a jury. None of your sons can do logic.

     

  4. Form a valid conclusion from the following statement: No kitten that loves fish is unteachable. No kitten with a tail will play with a gorilla. Kittens with whiskers always love fish. No teachable kitten has green eyes. No kittens have tails unless they have whiskers.

     

  5. Help Keith find the sugar addict. Make a truth table from the following statements:
    Keith: Three of you are always right. Who took one of my oatmeal pie cookies?
    Aurora: It was either Rita or Shirleen.
    Rita: Neither Jenny nor I took it.
    Shirleen: Both of you are wrong.
    Jamie: No, one is wrong; the other is right.
    Jenny: No, Jamie, that's not right.

     

  6. Fill in the truth table:
    ppp nand pp nor p~p
    00   
    11   

  7. Construct a truth table for ~p ^ q and ~p ^ ~q.
    pq~p~q~p ^ q~p ^ ~q
    00    
    01    
    10    
    11    

  8. Construct a truth table for [(p|q) ^ ~r] ^ r.
    pqrp|q~r(p|q) ^ ~r [(p|q) ^ ~r] ^ r
    000    
    001    
    010    
    011    
    100    
    101    
    110    
    111    

    Use the following story for the next four questions: When I was coming from St. Ives, I meet a man with 7 wives. Each wife had 7 sacks. Each sack had 7 cats. Each cat had 7 kits. Kits, cats, sacks, and wives, how many were going to St. Ives.

  9. Express this quantity in base seven.

  10. Calculate the quantity in base ten.

  11. Convert the base 7 quantity into base 10.

  12. How does this compare with the answer to the traditional wording (going to).

  13. Construct a "truth table" for the multiplication of positives and negatives.

  14. Write DeMorgan's Law using the logical symbols for and (^) and or () and overhead lines to represent the nots.

  15. See section 2.3 of your geometry textbook for further examples. See especially problems 2.3: 9-12.

  16. Bonus: Relative to crore, find out what numbers the following Hindu terms refer to: lakh, neel, padma, shankh.
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