Query Ass 4

course

I had some problems with this section. i am trying very hard to understand it. I think I am putting to much into it.

ލoYaassignment #004

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004. `Query 4

College Algebra

01-28-2007

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19:08:06

2.4.12 n(A') = 25, n(B) = 28, n(A' U B') = 40, n(A ^ B) = 10

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RESPONSE -->

I was stuck on problems 10 and 12 in the text. What was stumping me was the single prime numbers. I know where to put i.e. (AuB') but not n(A') I know were to put (A^B). You did not go over a Venn Diagram where you have a single prime number. Please explain it to me.

confidence assessment: 0

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19:17:29

** 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. **

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It says that (A 'u B ') = 40. If there are 15 in A and 10 in (A ^ B) and 18 in B, that adds up to 50. Do we subtract the 10 that intersect to get 40 to make the diagram true?

self critique assessment: 3

There are 28 in B, 18 of which are in B - A; I believe that's the 18 you are referring to. There are also 10 in A ^ B, as you note. There are 15 in A - B; in the set A we would also include the 10 in A ^ B, giving us 25 in set A.

The entire diagram consists of four regions. The union A U B consists of three regions: A - B (the part of A that isn't included in B), B - A (the part of B that isn't included in A) and A ^ B (the region where A and B overlap). The fourth region of the diagram is the region completely outside of A U B, and is most easily denoted (A U B) ' .

If you haven't already, you should sketch the picture and clearly label these regions for reference.

As I believe you see, B contains 28 elements, with 10 in the single region A ^ B and 18 in the single region B - A.

A' consists of two regions, B - A and and the 'fourth region' (A U B)'. Of the 25 elements in A ' we know that 18 are in B - A, which leaves 25 - 18 = 7 in (A U B) '.

So now we know the numbers of elements in three of the four single regions of the graph.

To get the fourth single region, note that A ' U B ' consists of everything that is either in A ' (i.e., outside of A) or B ' (i.e., outside of B). This includes the three labeled regions in your picture, which are (A U B) ' (which has 7 elements), B - A (with 18) and A - B (which we haven't yet figured out). The total number in these three regions is said to be 40, so the number in (A U B)' is 40 - 7 - 18 = 15.

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19:19:48

query 2.4.18 wrote and produced 2, wrote 5, produced 7 &&&& How many did he write but not produce?

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My answer is 5. I came up with that because if he wrote and composed 2 it can't be them and he produced 7 which if he only wrote and produced 2 then it would not be that either.

confidence assessment: 1

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19:22:38

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

He only wrote 5, two of which he also produced. So he wrote only 3 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 2 elements. This leaves 3 elements in the single region A - B and 5 elements in the single region B - A. The 3 elements in B - A would be the answer to the question. **

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RESPONSE -->

My first response to the question was to have 3 circles and that is what messed me up. 2 would be in the intersection leaving the rest to be determined. I don't why this is so hard for me to understand.

self critique assessment: 3

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19:26:51

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

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RESPONSE -->

You keep asking me the questions I can't answer, lol!

In the book it said that I need a circle for fat, for male, and for red. I made 3 circles and attempted to fill them in. (e) said that brown but not fat. I don't have a circle for brown and I did not know where to put the number. I need help with this one also.

confidence assessment: 0

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19:30:45

** 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.**

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RESPONSE -->

So I did not really even need a diagram for this. I was making it to hard.

self critique assessment: 3

I had the diagram when I wrote that, and would have had a very hard time figuring it out without the diagram. I think diagrams are pretty much necessary.

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I suggest that you move on to the next section and let these ideas 'setlle in' a bit, then come back to this one again.

The CD notes on this section should be helpful. Hopefully my notes will also help.

I'll be glad to answer additional questions.