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course Mth 151

²÷“¼ÚøÄÂ^¬—ţͧ˜ýðˆÊõ€ãÞîÁÐassignment #001

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001. `Query 1

College Algebra

06-04-2007

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14:06:13

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}

confidence assessment: 3

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14:06:21

**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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14:08:22

query 2.1.24 set builder for set of presidents between LBJ and Clinton

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RESPONSE -->

{xIx is the presidents between LBJ and Clinton}

confidence assessment: 3

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14:08:37

** 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: 2

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14:09:17

2.1.40 finite or infinite: set of rat #'s 0 to 1

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RESPONSE -->

Finite

confidence assessment: 3

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14:09:48

** 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

self critique assessment: 2

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14:11:31

2.1.48 n(A), A={x|x is a U.S. senator}

What is n(A) and why?

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RESPONSE -->

n(A) is the total number of U.S senators.

n(A) is 100 because there are two senators for each state.

confidence assessment: 3

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14:11:39

** 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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14:12:56

query 2.1.54 {x|x is neagtive number}

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RESPONSE -->

Well-defined

confidence assessment: 3

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14:13:09

** 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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14:13:44

2.1.72 true or false 2 not subset of {7,6,5,4}

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RESPONSE -->

True. 2 is not contained in the set, so it cannot be a subset.

confidence assessment: 3

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14:14:00

** 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

self critique assessment: 3

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14:14:35

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 that is not an element of B, so every element of C is not an element of B.

confidence assessment: OK

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14:14:45

** 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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Very good. Let me know if you have questions.