Query Assignment 1

#$&*

course Mth 151

001. `Query 1

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

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

List the elements of the set.

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

{4,5,6,7,8,9,10,11,12,13,14}

confidence rating #$&*:

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

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

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):

I put them in brackets is that correct???

@& Your answer is fine. But to clarify:

You were asked only to list the elements, so the brackets would be optional.

If asked to represent your listing as a set, the brackets would be required.*@

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

Self-critique Rating:

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

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

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

{36,37,38,39,40}

confidence rating #$&*:

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

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

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):

I didn't include LBJ or Clinton and I also used the number the president was not the name.

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

Self-critique Rating:

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

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

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

finite

confidence rating #$&*:

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

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

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):

Didn't understand this one at all. I will re-read the part of the chapter that has this in it. I am hoping that will help me understand it.

@& In a self-critique you want to address the specifics of the given solution, stating what you do and do not understand.

What did you make of the statement

'The subset {1/2, 1/3, 1/4, 1/5, ... } is just by itself an infinite set of rational numbers between 0 and 1. ' ?*@

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

Self-critique Rating:

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

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

What is n(A) and why?

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

n(A) = 100; because you have 2 senators for each state and we have 50 states.

confidence rating #$&*:

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

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

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:

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

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

 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

well-defined

@& You need to state why you think this is well-defined.*@

confidence rating #$&*:

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

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

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):

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

Self-critique Rating:

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

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:

True

@& On a question of this nature you need to say why you think the statement is true or false. It's very important to understand this on tests, where just a 'true' or a 'false' answer, without justification, is not given any credit.*@

confidence rating #$&*:

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

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

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 got the right answer but because I did the usual answer. After I read the common misconception I understood why the answer was true.

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

Self-critique Rating:

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

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:

False, because only two of the numbers in set C is in set B.

confidence rating #$&*:

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:

#(*!

&#This looks good. See my notes. Let me know if you have any questions. &#