query 1

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13:45:01 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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13:45:27 **A list of the elements would just be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. ** ......!!!!!!!!................................... RESPONSE --> this list gives all counting numbers between 4 and 14

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13:50:01 query 2.1.24 set builder for set of presidents between LBJ and Clinton ......!!!!!!!!................................... RESPONSE --> {LBJ, Nixon, ford, Carter, Reagan, Bush, Clinton} .................................................

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13:50:53 ** 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} ** ......!!!!!!!!................................... RESPONSE --> ok so i should have listed only one president?

Not quite. You should have used the phrase 'x is a president who served between Lyndon Johnson and William Clinton', which defines the criterion we use to judge whether x is in the set or not. If x = Ronald Reagan, then x meets this description and gets into the set. If x = George Washington, then x does not meet the description and won't be included in the set.

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13:51:04 2.1.40 finite or infinite: set of rat #'s 0 to 1 ......!!!!!!!!................................... RESPONSE --> finite

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13:51:43 ** 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. ** ......!!!!!!!!................................... RESPONSE --> so the correct answer would be infinite

Right. Be sure you understand the reason why.

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13:54:18 2.1.48 n(A), A={x|x is a U.S. senator} What is n(A) and why?

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RESPONSE --> {50} b/c there are fifty states and each state has one senator .................................................

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13:54:40 ** 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. ** ......!!!!!!!!................................... RESPONSE --> oh im sorry 2 for each state

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13:55:01 query 2.1.54 {x|x is neagtive number}

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RESPONSE --> well defined

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13:55:11 ** 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. ** ......!!!!!!!!................................... RESPONSE --> ok

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13:57:12 2.1.72 true or false 2 not subset of {7,6,5,4}

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RESPONSE --> true

'true' by itself is never a correct answer. Same with 'false' or 'yes' or 'no'.

Answers always need to be justified. All details of the solution and reasoning process must be given.

No problem here, but you need to know this for the test.

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13:58:15 ** 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. ** ......!!!!!!!!................................... RESPONSE --> 2 isn't a set and a subset must be a set .................................................

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13:58:58 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 12 is an element of c and not and element of b

Good.

This is an example of a well-documented answer.

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13:59:09 ** Specifically it's false because the element 12 is in C but not in B. ** ......!!!!!!!!................................... RESPONSE --> exactly

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ō攽滵愓}w臂w譮薕幦M壵轚褃箌 assignment #002 \枿堂覓M檾棡纫短藏袭簴醎牋� Liberal Arts Mathematics I 02-13-2006 "

You seem to be doing quite well here, but in some cases you want to provide a little more detail and justification in your answers and/or self-critiques.

Let me know if you have questions.