course Mth 151
6/19 10
Question: `qQuery 1.1.4 first 3 children male; conclusion next male. Inductive or deductive?YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Inductive because you are using a pattern to prove the conclustion
3
Ok
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Question: `qQuery 1.1.8 all men mortal, Socrates a man, therefore Socrates mortal.
Your solution:
Deductive because you are applying principals that since Socrates is a man and men are mortal then Socrates is mortal
3
Ok
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Question: `qQuery 1.1.20 1 / 3, 3 / 5, 5/7, 7/9, ... Probable next element.
Your solution:
9/11
3
Ok
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Question: `qQuery 1.1.23 This problem wasn't assigned, but you should be able to make a good attempt: 1, 8, 27, 64, ... What is the probable next element?
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Your solution:
64^3= 216
3
Ok
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Question: `qQuery 1.1.36 11 * 11 = 121, 111 * 111 = 12321 1111 * 1111 = 1234321; next equation, verify.
Your solution:
11111*11111= 123454321
3
Ok
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Question: `qDo you think this sequence would continue in this manner forever? Why or why not?
Your solution:
Yes because your multiplying by same think just adding a 1 each time
1
The answer is no because 9 10 9 would be 9109 which read 9 1 0 9 so the symmetry is messed up once you get into double digit numbers because 9 10 11 10 which is 9 1 0 1 1 1 0 not read the correct way
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Question: `qQuery 1.1.46 1 + 2 + 3 + ... + 2000 by Gauss' method
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Your solution:
Take the first number and pair it to the last then the second number to the first from last so it would be 1+2000=2001 and 2+1999=2001 so you would then take 2001*1000 because there are half as many pairs then numbers and you reach 2,001,000
3
Ok
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Question: `qQuery 1.1.57 142857 * 1, 2, 3, 4, 5, 6. What happens with 7? Give your solution to the problem as stated in the text.
Your solution:
They each have the same numbers but different order and multiplying by 7 breaks the pattern because you get 999999
3
Ok
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Question: `qWhat does this problem show you about the nature of inductive reasoning?
Your solution:
Basing something on a pattern is not always correct because patterns can be broken
3
Ok
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