Open QA 1

#$&*

course Mth 151

6/5 11

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. Sets

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

Question: `q001. Note that there are 4 questions in this assignment.

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

Question: `q001. Let A stand for the collection of all whole numbers which have at least one even digit (e.g., 237, 864, 6, 3972 are in the

collection, while 397, 135, 1, 9937 are not). Let A ' stand for the collection of all whole numbers which are not in the collection A. Let B stand for

the collection { 3, 8, 35, 89, 104, 357, 4321 }.

• What numbers do B and A have in common?

• What numbers do B and A' have in common?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

B and A would have in common that at least one number would be even.

I don’t see a resemblance in these 2 other than all the numbers in a’ are in b but there are even numbers in b.

confidence rating #$&*:

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

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

Given Solution:

Of the numbers in B, 8, 89, 104, 4321 each have at least one even digit and so are common to both sets.

Of the numbers in B, 3 is odd, both of the digits in the number 35 are odd, as are all three digits in the number 357. All three of these numbers are therefore in A ' .

STUDENT QUESTION

In the second part of the question you said BOTH of these numbers are therefore in A’, so does that mean that 3 is not and if so then why not?

Also what does the ‘ (is it an apostrophe?) in A’ stand for or is in just a means of separation? INSTRUCTOR RESPONSE

Of the numbers in B, the number 3 is in A ', the number 35 is in A ' and the number 357 is in A ' .  The apostrophe (you identified it

correctly) indicates that you are looking for elements that are NOT in the set. This is in relation to the statement in the problem: Let

A ' stand for the collection of all whole numbers which are not in the collection A.

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

Self-critique (if necessary):

I don’t really understand the correct answer to the second part.

@&

When you don't understand part of a given solution, you need to deconstruct it and tell me as much as you can about that part of the solution, and what you do and do not understand about it.

The given solution tells you the following:

Of the numbers in B, 3 is odd, both of the digits in the number 35 are odd, as are all three digits in the number 357. All three of these numbers are therefore in A ' .

The first sentence is

'Of the numbers in B, 3 is odd, both of the digits in the number 35 are odd, as are all three digits in the number 357.

Can you tell me specifically what you do and do not understand about this sentence?

What do you and do you not understand how this statement could be relevant to whether these elements are in A ' ?

Do you understand why 3 is in A ' ?
Do you understand why 35 is in A ' ?
Do you understand why 357 is in A ' ?

*@

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

Self-critique Rating:2

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

Question: `q002. I have in a room 8 people with dark hair brown, 2 people with bright red hair, and 9 people with light brown or blonde hair. Nobody

has more than one hair color. Is it possible that there are exactly 17 people in the room?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

No. Since nobody has more than one hair color and that each color is an independent color, there’s no way.

9 + 8 + 2 =19 people.

confidence rating #$&*:

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

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

Given Solution:

`aIf we assume that dark brown, light brown or blonde, and bright red hair are mutually exclusive (i.e., someone can't be both one category and

another, much less all three), then we have at least 8 + 2 + 9 = 19 people in the room, and it is not possible that we have exactly 17.

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

Self-critique (if necessary):

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

Self-critique Rating:

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

Question: `q003. I have in a room 6 people with dark hair and 10 people with blue eyes. There are only 14 people in the room. But 10 + 6 = 16, which

is more than 14. How can this be?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

There are at least 2 people with dark hair and blue eyes.

confidence rating #$&*:

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

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

Given Solution:

`aThe key here is that there is nothing mutully exclusive about these categories-a person can have blue eyes as well as dark hair. So if there are 2

people in the room who have dark hair and blue eyes, which is certainly possible, then when we add 10 + 6 = 16 those two people would be counted

twice, once among the 6 blue-eyed people and once among the 10 dark-haired people. So the 16 we get would be 2 too high. To get the correct number we

would have to subtract the 2 people who were counted twice to get 16 - 2 = 14 people.

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

Self-critique (if necessary):

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

Self-critique Rating:

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

Question: `q004. In a set of 100 child's blocks 60 blocks are cubical and 40 blocks are cylindrical. 30 of the blocks are red and 20 of the red blocks

are cubical. How many of the cylindrical blocks are red?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

10 cylindrical blocks are red.

confidence rating #$&*:

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

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

Given Solution:

`aOf the 30 red blocks 20 are cubical, so the rest must be cylindrical. This leaves 10 red cylindrical blocks.

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

Self-critique (if necessary):

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

Self-critique Rating:

Self-critique (if necessary):

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

Self-critique rating:

Self-critique (if necessary):

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

Self-critique rating:

#*&!

Open QA 1

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