#$&* course Mth 151 1/18 8 004. `Query 4*********************************************
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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): This explanation makes sense. I should be able to figure out any similar problems now. ------------------------------------------------ Self-critique Rating:0 ********************************************* Question: `qquery 2.4.19 wrote and produced 3, wrote 5, produced 7 &&&& How many did he write but not produce? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I looked up this problem in the book. The book says that he wrote and produced 2 projects. I’ve tried to work it with 3 and with 2. When I work it with 2 as the number of projects both written and produced, I take 2 away from 5 and 7. This leaves 3+5+2=10. 10 is the number of projects altogether. When I worked the problem for 3 however, I take 3 away from both 5 and 7. This leaves, 2+4+3=9. So because of this, I’m going to work it for 2 and say that there were 3 projects that the guy wrote but did not produce. If I work it for 3 instead, he will have written but not produced 2. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ------------------------------------------------ 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: There are 48 FAT Chickens. There are 22 RED Chickens. There are 59 MALE Chickens. There are 13 chickens who are Fat but not Males. There are 7 Chickens who are brown but not fat. There are 11 Chickens who are red and fat. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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.** I felt pretty confident about my answers. The only one that I can see clearly how I mess up is the one about how many chickens are brown not fat. In that problem, I forgot to add the roosters. I used a Venn diagram… Oh Aha!! I just found a problem. … I did not split up the fat roosters from the Fat, red roosters. Okay. That’s probably the main problem with my work. I need to pay better attention. " end document 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: There are 48 FAT Chickens. There are 22 RED Chickens. There are 59 MALE Chickens. There are 13 chickens who are Fat but not Males. There are 7 Chickens who are brown but not fat. There are 11 Chickens who are red and fat. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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.** I felt pretty confident about my answers. The only one that I can see clearly how I mess up is the one about how many chickens are brown not fat. In that problem, I forgot to add the roosters. I used a Venn diagram… Oh Aha!! I just found a problem. … I did not split up the fat roosters from the Fat, red roosters. Okay. That’s probably the main problem with my work. I need to pay better attention. " end document 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: There are 48 FAT Chickens. There are 22 RED Chickens. There are 59 MALE Chickens. There are 13 chickens who are Fat but not Males. There are 7 Chickens who are brown but not fat. There are 11 Chickens who are red and fat. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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.** I felt pretty confident about my answers. The only one that I can see clearly how I mess up is the one about how many chickens are brown not fat. In that problem, I forgot to add the roosters. I used a Venn diagram… Oh Aha!! I just found a problem. … I did not split up the fat roosters from the Fat, red roosters. Okay. That’s probably the main problem with my work. I need to pay better attention. " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!