course Mth 151 sº’üßäë뎞՛µûäðÓ¡¤„’Ùassignment #006
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20:59:22 Query 1.1.4 first 3 children male; conclusion next male. Inductive or deductive?
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RESPONSE --> inductive because having 3 boys first does not necessarily mean she will have another boy. confidence assessment: 3
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20:59:33 ** The argument is inductive, because it attempts to argue from a pattern. **
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RESPONSE --> Right self critique assessment: 3
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21:00:10 Query 1.1.8 all men mortal, Socrates a man, therefore Socrates mortal.
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RESPONSE --> deductive because it states that all men are mortal so Socrates falls in the category of being a male confidence assessment: 3
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21:00:39 ** this argument is deductive--the conclusions follow inescapably from the premises. 'all men' is general; 'Socrates' is specific. This goes general to specific and is therefore deductive. COMMON ERROR: because it is based on a fact, or concrete evidence. Fact isn't the key; the key is logical inevitability. The argument could be 'all men are idiots, Socrates is an man, therefore Socrates is an idiot'. The argument is every bit as logical as before. The only test for correctness of an argument is that the conclusions follow from the premises. It's irrelevant to the logic whether the premises are in fact true. **
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RESPONSE --> Understand self critique assessment: 3
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21:02:16 Query 1.1.20 1 / 3, 3 / 5, 5/7, ... Probable next element.
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RESPONSE --> 7/9, they are adding 2 to the numerator and 2 to the demoniator confidence assessment: 3
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21:02:45 **The numbers 1, 3, 5, 7 are odd numbers. We note that the numerators consist of the odd numbers, each in its turn. The denominator for any given fraction is the next odd number after the numerator. Since the last member listed is 5/7, with numerator 5, the next member will have numerator 7; its denominator will be the next odd number 9, and the fraction will be 7/9. There are other ways of seeing the pattern. We could see that we use every odd number in its turn, and that the numerator of one member is the denominator of the preceding member. Alternatively we might simply note that the numerator and denominator of the next member are always 2 greater than the numerator and denominator of the present member. **
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RESPONSE --> Okay self critique assessment: 3
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21:05:28 Query 1.1.23 1, 8, 27, 64, ... Probable next element.
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RESPONSE --> 216 confidence assessment: 0
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21:06:55 ** This is the sequence of cubes. 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125. The next element is 6^3 = 216. Successive differences also work: 1 8 27 64 125 .. 216 7 19 37 61 .. 91 12 18 24 .. 30 6 6 .. 6 **
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RESPONSE --> I could not figure out the sequence so I am glad you helped on that one self critique assessment: 3
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21:08:24 Query 1.1.36 11 * 11 = 121, 111 * 111 = 12321 1111 * 1111 = 1234321; next equation, verify.
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RESPONSE --> 11111*11111=12,345,321, all that needed be done was to follow the sequence which was to keep adding a one and multiply that times itself. confidence assessment: 3
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21:08:34 ** We easily verify that 11111*11111=123,454,321 **
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RESPONSE --> right self critique assessment: 3
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21:09:05 Do you think this sequence would continue in this manner forever? Why or why not?
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RESPONSE --> Yes because the pattern or sequence was never broken confidence assessment: 3
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21:09:45 ** You could think forward to the next few products: What happens after you get 12345678987654321? Is there any reason to expect that the sequence could continue in the same manner? The middle three digits in this example are 8, 9 and 8. The logical next step would have 9, 10, 9, but now you would have 9109 in the middle and the symmetry of the number would be destroyed. There is every reason to expect that the pattern would also be destroyed. **
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RESPONSE --> so we don't change the pattern self critique assessment: 3
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21:11:19 Query 1.1.46 1 + 2 + 3 + ... + 2000 by Gauss' method
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RESPONSE --> 2,001,000 If they ar egoing to 2000 then we know that half that is 1000. Then with the Gauss' method we multiply that by 2001 confidence assessment: 3
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21:11:27 ** Pair up the first and last, second and second to last, etc.. You'll thus pair up 1 and 2000, 2 and 1999, 3 and 1998, etc.. Each pair of numbers totals 2001. Since there are 2000 numbers there are 1000 pairs. So the sum is 2001 * 1000 = 2,001,000 **
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RESPONSE --> Good self critique assessment: 3
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21:12:07 Query 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.
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RESPONSE --> they all keep the same digits, 999,999 confidence assessment: 3
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21:13:29 ** Multiplying we get 142857*1=142857 142857*2= 285714 142857*3= 428571 142857*4=571428 142857*5= 714285 142857*6=857142. Each of these results contains the same set of digits {1, 2, 4, 5, 7, 8} as the number 1428785. The digits just occur in different order in each product. We might expect that this pattern continues if we multiply by 7, but 142875*7=999999, which breaks the pattern. **
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RESPONSE --> that is wierd that the pattern was broken at 7. You would think that it would keep going although the more you multply the bigger the number gets so it goes beyond 6 digits self critique assessment: 3
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21:15:05 What does this problem show you about the nature of inductive reasoning?
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RESPONSE --> That inductive reasoning can be misconstrued and just when you think the next outcome is the same as the previous, the BAM it does not work like planned. confidence assessment: 3
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21:15:24 ** Inductive reasoning would have led us to expect that the pattern continues for multiplication by 7. Inductive reasoning is often correct it is not reliable. Apparent patterns can be broken. **
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RESPONSE --> Yes they can self critique assessment: 3
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