course MTH 151 Monday, September 14 at 11:15 001. `Query 1vvvv
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: { 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 } confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
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Given Solution: `a**A list of the elements would just be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `qquery 2.1.24 listing for set of presidents between LBJ and Clinton
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: { x/x is the presidents who served between LBJ and Clinton } confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 1
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Given Solution: `a** A listing would be {}{}{Lyndon Johnson, Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Regan, George HW Bush, William Clinton}.{}{}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} ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I think I was rather close to the given solution I would have listed them but I didn't know them so I used set-builder notation ( I should learn my presidents). I also don't know how to type the vertical line which makes my answer look like ""x divided by x"" but that is not what I intended it to be. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q2.1.40 finite or infinite: set of rat #'s 0 to 1
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The set of all numbers from 0 to 1. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): The given solution was very detailed. I simply gave a word description designating that the set was infinite. I was quite sure that it was correct, but I doubt it more after reading the given solution. ------------------------------------------------ Self-critique Rating: 2 ********************************************* Question: `q2.1.48 n(A), A={x|x is a U.S. senator} What is n(A) and why?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: n(A) = 100 because ""n(A)"" refers to the cardinal number in the set, so sense there are 100 U.S. senators the and none of them are senators from more than one state then n(A) = 100. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 2
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `qquery 2.1.54 {x|x is neagtive number}
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: This set is well-defined because it is possible to determine if a number is negative or not. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 2
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q2.1.74 (formerly 2.1.72) This was not assigned, but you should be able to answer based on your work on similar problems: It is or is it not true that 2 is not not subset of {7,6,5,4}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: It is true that 2 is not a subset of {7,6,5,4} because the numbers are clearly listed and 2 is not one of them. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Well I guess I made a common misconception. However it was easy to make because the question in the book asks if it is true or false that 2 is not an element of {7, 6, 5, 4}. I feel that this was misleading.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: It is false, because set B does not contain 12. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3
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Given Solution: `a** Specifically it's false because the element 12 is in C but not in B. ** "