course Mth 151 JÔVGDÏ֓assignment #001
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13:17:52 Query 2.1.12 counting #'s 4 to 14 List the elements of the set.
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RESPONSE --> Well, the listing method gives us this for a set (4, 5,6,7,8,9,10,11,12,13,14) So the elements would be: 4,5,6,7,8,9,10,11,12,13,14 I am confident in my answer, all I had to do was write it in listing method form, and I received the answer. confidence assessment: 3
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13:18:02 **A list of the elements would just be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. **
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RESPONSE --> OK self critique assessment: 3
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13:21:31 query 2.1.24 set builder for set of presidents between LBJ and Clinton
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RESPONSE --> Without looking up the lineage of presidents, I deduced that JFK was president right before LBJ was elected into office, and that Bush is the most current president after clinton. So using previous knowledge of presidents, I came up with [x\x is a president after LBJ and before Clinton] [Nixon, Ford, Carter, Reagan, Bush] confidence assessment: 3
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13:21:54 ** Set-builder notation is {x|x is a president who served between Lyndon Johnson and William Clinton} x is a variable and the condition 'x is a president who served between Lyndon Johnson and William Clinton' tells you what possible things the variable can be. COMMON ERROR: It's incorrect to say {x | x is the set of presidents who served between Johnson and Clinton}. x is a president, not a set of presidents. Should be {x|x is a president who served between Lyndon Johnson and William Clinton} **
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RESPONSE --> OK self critique assessment: 3
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13:23:12 2.1.40 finite or infinite: set of rat #'s 0 to 1
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RESPONSE --> Since we are able to count those numbers up to 1, and they eventually reach an end when we count from 0, that makes it finite. confidence assessment: 3
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13:24:28 ** Rational numbers have form p/q, where p and q are integers. Numbers like 5/8, 57/31, -3/5, -57843/7843, etc. The subset {1/2, 1/3, 1/4, 1/5, ... } is just by itself an infinite set of rational numbers between 0 and 1. Then you have things like 348/937, and 39827389871 / 4982743789, and a whole infinite bunch of others. There are thus infinitely many rational numbers in any interval of the real line. COMMON MISCONCEPTION: finite, because it doesn't go on forever Rational numbers have form p/q, where p and q are integers. Numbers like 5/8, 57/31, -3/5, -57843/7843, etc. Not all of these lie between 0 and 1, of course. **
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RESPONSE --> I fell into the trap of the common misconception, excluding the vast possabilities that rational numbers hold. I will remember this in future problems. self critique assessment: 2
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13:25:32 2.1.48 n(A), A={x|x is a U.S. senator} What is n(A) and why?
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RESPONSE --> The cardinal number of A, which is the set of U.S senators, is 100, being that there are two state senators per state. n(A)=100 confidence assessment: 2
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13:25:48 ** n(A) stands for the number of elements in the set--in this case for the number of senators. There are 100, 2 from each State. So n(A) = 100. **
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RESPONSE --> OK self critique assessment: 3
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13:26:51 query 2.1.54 {x|x is neagtive number}
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RESPONSE --> This is a well defined ansewr, because it makes it absolutely certain that the elements of the set will be negative. I am sure this answer is correct, confidence assessment: 3
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13:27:09 ** This notation means all possible values of x such that x is a negative number. The question is whether the set is well-defined or not. It is in fact well-defined because there is a definite way to decide whether a given object is an element of the set, because there is a definite way to determine whether an object is a negative number or not. ALTERNATIVE ANSWER: The set is well-defined because you have a criterion by which you can definitely decide whether something is or is not in the set. **
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RESPONSE --> OK self critique assessment: 3
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13:28:10 2.1.72 true or false 2 not subset of {7,6,5,4}
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RESPONSE --> True, 2 is not an element of the set (7,6,5,4) So of course, if it's not even an included element, it can't be a subset at all. confidence assessment: 3
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13:29:33 ** The statement is that 2 is not a subset. The statement is true because 2 isn't even a set, it's just a number. {2} is a set and could be a subset of something. 2 is just a number; it isn't a set so it can't be a subset of anything. The usual answer is that 2 isn't a subset because 2 isn't in the set. However that's not the correct reason. The correct reason is that 2 isn't a set and a subset must be a set. COMMON MISCONCEPTION: the statement says that 2 is not a subset, not that it is not an element of the set. So the reason it's not a subset is that 2 isn't a set at all, so it can't be a subset of anything. **
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RESPONSE --> Very tricky answer, I completely missed the fact that it was 2, not (2). I will be more careful and critical in my thinking regarding future similar problems. self critique assessment: 2
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13:30:44 2.1.84 C={4,10,12}, B={2,4,8,10} Is it true or false that every element of C is also an element of B?
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RESPONSE --> False, every element of C cannot be an element of B. They have 4 and 10 in common, but not 12, 12 is not shared between them at all, so the the statement is FALSE. confidence assessment: 3
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13:30:52 ** Specifically it's false because the element 12 is in C but not in B. **
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RESPONSE --> OK self critique assessment: 3
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