Assignment 2

course Mth 151

y??\?????????assignment #001

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

001. `Query 1

College Algebra

01-21-2007

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03:54:56

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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03:58:31

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

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RESPONSE -->

(Nixon, Ford, Carter, Reagan, Bush)

confidence assessment: 3

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04:05:00

** 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 mistook set building notation and regular listing.

self critique assessment: 2

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04:07:04

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

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RESPONSE -->

Infinite.

confidence assessment: 3

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04:07:37

** 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: 3

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04:12:31

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)=100. n(A) is the cardinality of the set and you only count each item once.

confidence assessment: 3

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04:12:51

** 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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04:16:48

query 2.1.54 {x|x is neagtive number}

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RESPONSE -->

{-1, -2, -3, ...}

confidence assessment: 3

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04:18:49

** 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 -->

I didn't realize the question was asking about definition.

self critique assessment: 2

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04:24:12

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

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RESPONSE -->

True.

confidence assessment: 3

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04:26:23

** 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 -->

I didn't put my reason for true, but the subset term wouldn't have entered my thinking.

self critique assessment: 2

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04:29:42

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. C has two of the same numbers as B, but B does not have the number 12.

confidence assessment: 3

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04:29:56

** 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

.................................................

"

Good responses--you appear to be in good shape here. Let me know if you have questions.

Assignment 2

course Mth 151

y??\?????????assignment #001

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

001. `Query 1

College Algebra

01-21-2007

......!!!!!!!!...................................

03:54:56

Query 2.1.12 counting #'s 4 to 14

List the elements of the set.

......!!!!!!!!...................................

RESPONSE -->

(4,5,6,7,8,9,10,11,12,13,14)

confidence assessment: 3

.................................................

......!!!!!!!!...................................

03:58:31

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

......!!!!!!!!...................................

RESPONSE -->

(Nixon, Ford, Carter, Reagan, Bush)

confidence assessment: 3

.................................................

......!!!!!!!!...................................

04:05:00

** 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 -->

I mistook set building notation and regular listing.

self critique assessment: 2

.................................................

......!!!!!!!!...................................

04:07:04

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

......!!!!!!!!...................................

RESPONSE -->

Infinite.

confidence assessment: 3

.................................................

......!!!!!!!!...................................

04:07:37

** 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 -->

Ok.

self critique assessment: 3

.................................................

......!!!!!!!!...................................

04:12:31

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

What is n(A) and why?

......!!!!!!!!...................................

RESPONSE -->

n(A)=100. n(A) is the cardinality of the set and you only count each item once.

confidence assessment: 3

.................................................

......!!!!!!!!...................................

04:12:51

** 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 -->

Ok.

self critique assessment: 3

.................................................

......!!!!!!!!...................................

04:16:48

query 2.1.54 {x|x is neagtive number}

......!!!!!!!!...................................

RESPONSE -->

{-1, -2, -3, ...}

confidence assessment: 3

.................................................

......!!!!!!!!...................................

04:18:49

** 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 -->

I didn't realize the question was asking about definition.

self critique assessment: 2

.................................................

......!!!!!!!!...................................

04:24:12

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

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RESPONSE -->

True.

confidence assessment: 3

.................................................

......!!!!!!!!...................................

04:26:23

** 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 -->

I didn't put my reason for true, but the subset term wouldn't have entered my thinking.

self critique assessment: 2

.................................................

......!!!!!!!!...................................

04:29:42

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?

......!!!!!!!!...................................

RESPONSE -->

False. C has two of the same numbers as B, but B does not have the number 12.

confidence assessment: 3

.................................................

......!!!!!!!!...................................

04:29:56

** Specifically it's false because the element 12 is in C but not in B. **

......!!!!!!!!...................................

RESPONSE -->

Ok.

self critique assessment: 3

.................................................

"

Good responses--you appear to be in good shape here. Let me know if you have questions.