assignment 04 query

#$&*

course MTH 151

9/22/14 around 8:54 pm

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.

004. `Query 4

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

Question: `q2.4.13 (formerly 2.4.12) This was not assigned but you answered similar questions and should be

able to answer this one: n(A') = 25, n(B) = 28, n(A' U B') = 40, n(A ^ B) = 10. What is n(A - B)?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

N(A-B)=15

If the intersect of A and B is 10 then there are 18 in B that aren’t in A

There are 25 outside of A and 18 are in B then 25-18=7 which are outside of both A and B

A’ U B’ is everything that isn’t in A and everything that isn’t in B so that would be everything except the

intersection of A and B so 40=18 (region B) +7 (region outside of A and B) + x (region A)

40=25+x

15=x

A=15

confidence rating #$&*: 3

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

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

Given Solution:

`a** In terms of the picture (2 circles, linked, representing the two sets) there are 28 in B and 10 in A ^ B

so there are 18 in the region of B outside of A--this is the region B-A.

There are 25 outside of A, and 18 of these are accounted for in this region of B. Everything else outside of A

must therefore also be outside of B, so there are 25-18=7 elements in the region outside of both A and B.

A ' U B ' consists of everything that is either outside of A or outside of B, or both. The only region that's

not part of A ' U B ' is therefore the intersection A ^ B, since everything in this region is inside both sets.

A' U B' is therefore everything but the region A ^ B which is common to both A and B. This includes the 18

elements in B that aren't in A and the 7 outside both A and B. This leaves 40 - 18 - 7 = 15 in the region of A

that doesn't include any of B. This region is the region A - B you are looking for.

Thus n(A - B) = 40 - 18 - 7 = 15.**

Supplementary comments:

For example, with (A' U B'), you ask the following questions in order:

What regions are in A?

What regions are therefore in A'?

What regions are in B?

What regions are therefore in B'?

So, what regions are in A' U B'?

If you can break a question down to a series of simpler questions, you can figure out just about anything.

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

Self-critique (if necessary):ok

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

Self-critique Rating:ok

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

Question: `qquery 2.4.19 wrote and produced 3, wrote 5, produced 7 &&&& How many did he write but not

produce?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

He wrote 2 without producing them.

If he wrote a total of 5 and only produced 3 then that leaves 2

confidence rating #$&*: 3

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

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

Given Solution:

`a** You need to count the two he wrote and produced among those he wrote, and also among those he produced.

He only wrote 5, three of which he also produced. So he wrote only 2 without producing them.

In terms of the circles you might have a set A with 5 elements (representing what he wrote), B with 7 elements

(representing what he produced) and A ^ B with 3 elements. This leaves 2 elements in the single region A - B

and 5 elements in the single region B - A. The 2 elements in B - A would be the answer to the question. **

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

Self-critique (if necessary):ok

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

Self-critique Rating:ok

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

Question: `q2.4.25 (formerly 2.4.24) 9 fat red r, 18 thn brown r, 2 fat red h, 6 thin red r, 26 fat r, 5 thin

red h, 37 fat, 7 thin brown hens. ......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

37 chickens are fat

Red? 22

9 fat r r + 2 fat r h + 6 thin r r + 5 thin r h

Male? 50

26 fat r +18 b r + 6 thin r r = 50

We do not count the 9 fat red roosters since that is included in the 26 fat roosters

Fat, but not male? 11

37 total fat chickens - 26 fat roosters = 11 fat hens

Brown but not fat? 25

18 thin b r + 7 thin b h = 25

Red and fat? 11

9 fat r r + 2 fat red h = 11

confidence rating #$&*: 3

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

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

Given Solution:

`a** Here's my solution. Tell me if there is anything you disagree with (I'm not infallible) or don't

understand.

incidental: 18 thin brown roosters, 7 thin brown hens, 6 thin red hens and the 6 thin roosters which aren't

fat (out of the 50-26=24 thin roosters 18 are brown so 6 are red) adds up to 37 thin chickens

How many chickens are fat?

37 as given

How many chickens are red?

22: 9 fat red roosters, 6 thin red roosters, 5 thin red hens, 2 fat red hens.

How many chickens are male?

50: 9 fat red roosters are counted among the 26 fat roosters so the remaining 17 fat roosters are brown; then

there are 18 thin brown roosters and 6 thin red roosters; the number of roosters therefore adds up to 9 + 18 +

6 + 17 = 50

How many chickens are fat not male?

26 of the 37 fat chickens are male, leaving 11 female

How many chickens are brown not fat?

25: 18 thin brown roosters, 7 thin brown hens adds up to 25 thin brown chickens

How many chickens are red and fat?

11: 9 fat red roosters and 2 fat red hens.**

"

Self-critique (if necessary):

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

Self-critique rating:

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

Question: `q2.4.25 (formerly 2.4.24) 9 fat red r, 18 thn brown r, 2 fat red h, 6 thin red r, 26 fat r, 5 thin

red h, 37 fat, 7 thin brown hens. ......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

37 chickens are fat

Red? 22

9 fat r r + 2 fat r h + 6 thin r r + 5 thin r h

Male? 50

26 fat r +18 b r + 6 thin r r = 50

We do not count the 9 fat red roosters since that is included in the 26 fat roosters

Fat, but not male? 11

37 total fat chickens - 26 fat roosters = 11 fat hens

Brown but not fat? 25

18 thin b r + 7 thin b h = 25

Red and fat? 11

9 fat r r + 2 fat red h = 11

confidence rating #$&*: 3

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

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

Given Solution:

`a** Here's my solution. Tell me if there is anything you disagree with (I'm not infallible) or don't

understand.

incidental: 18 thin brown roosters, 7 thin brown hens, 6 thin red hens and the 6 thin roosters which aren't

fat (out of the 50-26=24 thin roosters 18 are brown so 6 are red) adds up to 37 thin chickens

How many chickens are fat?

37 as given

How many chickens are red?

22: 9 fat red roosters, 6 thin red roosters, 5 thin red hens, 2 fat red hens.

How many chickens are male?

50: 9 fat red roosters are counted among the 26 fat roosters so the remaining 17 fat roosters are brown; then

there are 18 thin brown roosters and 6 thin red roosters; the number of roosters therefore adds up to 9 + 18 +

6 + 17 = 50

How many chickens are fat not male?

26 of the 37 fat chickens are male, leaving 11 female

How many chickens are brown not fat?

25: 18 thin brown roosters, 7 thin brown hens adds up to 25 thin brown chickens

How many chickens are red and fat?

11: 9 fat red roosters and 2 fat red hens.**

"

Self-critique (if necessary):

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

Self-critique rating:

#*&!

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