course MTH 151 Monday Sept. 14 at 11:21 vvvv
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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. ** Supplementary comments:
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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, 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 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: I made a Venn Diagram with three circles representing chickens that are fat, male, or red made up of seven regions: Region I has chickens that are fat but not red or male which = 19, region II has chickens that are male but not fat or red = 18, region III has chickens that are red but not fat or male, region IV has chickens that are both fat and male but not red = 7, region V has chickens that are fat and red but not male = 2, region VI has chickens that are red and male but not fat = 6, and region VII has chickens that are fat, male and red = 9. Fat= 37 Red= 5 + 2 + 6 + 9 = 22 Male= 18 + 7 + 6 + 9 = 40 Fat, not male= 2 + 9= 11 Brown, not fat= 7 + 18= 25 Red and fat= 2 + 9=11 confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 2
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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.**