course Mth 151
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10:58:21 Query 2.1.12 counting #'s 4 to 14 List the elements of the set.
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RESPONSE --> {4,5,6,7,8,9,10,11,12,13,14}
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10:58:29 **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
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11:03:14 query 2.1.24 set builder for set of presidents between LBJ and Clinton
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RESPONSE --> {Johnson, Nixon, Ford, Carter, Reagan, Bush, Clinton}
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11:04:17 ** 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 misunderstood the question, i thought it was asking for the elements of the set.
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11:04:40 2.1.40 finite or infinite: set of rat #'s 0 to 1
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RESPONSE --> finite
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11:05:26 ** 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 --> ok
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11:07:15 2.1.48 n(A), A={x|x is a U.S. senator} What is n(A) and why?
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RESPONSE --> A is 100 because there are 100 US senators, 2 for each state and there are 50 states.
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11:07:26 ** 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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11:07:43 query 2.1.54 {x|x is neagtive number}
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RESPONSE --> well defined
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11:07:54 ** 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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11:08:07 2.1.72 true or false 2 not subset of {7,6,5,4}
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RESPONSE --> true
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11:08:19 ** 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 --> ok
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11:08:31 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
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11:08:38 ** 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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