course Mth 151 ¬¢Òp|\¬ÇFʵ³šÔ’‹› –oÕ©|assignment #001
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21:08:22 Query 2.1.12 counting #'s 4 to 14 List the elements of the set.
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RESPONSE --> {4, 5, 6, 7, ..., 14}
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21:09:06 **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 - I was supposed to just list the numbers instead of making them into a set.
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21:09:48 query 2.1.24 set builder for set of presidents between LBJ and Clinton
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RESPONSE --> {Nixon, Ford, Carter, Regan, Bush}
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21:12:45 ** 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 --> I just named the set. For ""set-builder notation"" I need to use the ""x l x"" statement. {x l x is a president that served between LBJ and Clinton}
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21:14:23 2.1.40 finite or infinite: set of rat #'s 0 to 1
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RESPONSE --> finite ""Set of rational numbers 0 to 1"" gives a set beginning and a set end. If there was not an ending it would be infinite.
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21:19:17 ** 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 honestly have no idea what p/q means or what a rational number is for that matter. Oh... rational numbers are fractions? I understand now, I think. The correct answer is infinite because there are countless rational numbers between 0 and 1. The fractions just get smaller and smaller. Right?
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21:23:32 2.1.48 n(A), A={x|x is a U.S. senator} What is n(A) and why?
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RESPONSE --> There are 100 U. S. senators. n = the total number of elements in a set. n(A) = 100 {1 senator, 2 senator, 3 senator, 4 senator, ..., 100 senator} The total elements in this set are 100. So the cardinality is 100.
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21:23:46 ** 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
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21:25:16 query 2.1.54 {x|x is neagtive number}
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RESPONSE --> This is well-defined. The person reading it will know what it means and there is no misunderstanding or assumptions. x = all negative numbers
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21:25:47 ** 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
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21:30:51 2.1.72 true or false 2 not subset of {7,6,5,4}
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RESPONSE --> This is true because 2 is not included in the set of numbers. The only way it would be correct is if you picked a number from that set.
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21:36:51 ** 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 --> 2 cannot be a subset of a set because it is not even a set. It is just a number. The book on page 52 explains this differently. It doesn't say anything about subsets. It says that E ""is an element of"" and that slash E means ""is not an element of.""
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21:41:50 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 --> This is false. Every element in set C has to be in set B also. 4 and 10 match, but set C also has 12 which is not in set B.
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21:41:57 ** Specifically it's false because the element 12 is in C but not in B. **
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RESPONSE --> ok
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