Open query 1

#$&*

course Mth 151

1/23

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

001. `Query 1

*********************************************

Question: `qQuery 2.1.12 counting #'s 4 to 14

List the elements of the set.

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The elements would be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

Given Solution:

`a**A list of the elements would just be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:3

*********************************************

Question: `qquery 2.1.24 listing for set of presidents between LBJ and Clinton

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

{x|x is a president who served between LBJ and Clinton.

{ Lyndon Johnson, Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Regan, George HW Bush, William Clinton}

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

Given Solution:

`a** A listing would be {}{}{Lyndon Johnson, Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Regan, George HW Bush, William Clinton}.{}{}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} **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:3

*********************************************

Question: `q2.1.40 finite or infinite: set of rat #'s 0 to 1

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Infinite because it includes everything between 0 and 1

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

Given Solution:

`a** 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. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

I left a few things out, but understand the concept.

------------------------------------------------

Self-critique Rating:3

*********************************************

Question: `q2.1.48 n(A), A={x|x is a U.S. senator}

What is n(A) and why?

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

N is equal to the number in a set and A = a U.S. senator

There is 100 US senators so n(A)=100

confidence rating #$&*: 2

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

Given Solution:

`a** 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. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:3

*********************************************

Question: `qquery 2.1.54 {x|x is neagtive number}

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

This is saying the set is a negative number.

confidence rating #$&*: 2

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

Given Solution:

`a** 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. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

I got the answer…just in my own words I guess you could say.

------------------------------------------------

Self-critique Rating:3

*********************************************

Question: `q2.1.74 (formerly 2.1.72) This was not assigned, but you should be able to answer based on your work on similar problems: It is or is it not true that 2 is not not subset of {7,6,5,4}?

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

2 is not a subset because it is not in the set {7,6,5,4}

confidence rating #$&*:3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

Given Solution:

`a** 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. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

I put the usual answer in, but I understand

------------------------------------------------

Self-critique Rating:3

*********************************************

Question: `q2.1.86 (formerly 2.1.84). This was not assigned but you did answer several questions related to the sets C={4,10,12}, B={2,4,8,10}, and should be able to answer this.

Is it true or false that every element of C is also an element of B? Be sure to include your reasoning.

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

It is false because B does not include 12.

confidence rating #$&*:3

*********************************************

Question: `q2.1.86 (formerly 2.1.84). This was not assigned but you did answer several questions related to the sets C={4,10,12}, B={2,4,8,10}, and should be able to answer this.

Is it true or false that every element of C is also an element of B? Be sure to include your reasoning.

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

It is false because B does not include 12.

confidence rating #$&*:3

#(*!

&#Good work. Let me know if you have questions. &#