#$&* course MTH 151 Time of submission: 10:02 PM, 22 January 2012 If your solution to stated problem does not match the given solution, you should self-critique per instructions athttp://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm
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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): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qquery 2.4.19 wrote and produced 3, wrote 5, produced 7 &&&& How many did he write but not produce? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: - Out of the ten projects that Mr. Long had worked on, five were written, two were written and produced; obviously this means that three were only written. - As far as the Venn Diagram went, I only drew two to symbolize the projects he wrote (A) being 5, those he produced (B) being 7, along with those he wrote and produced (A ^ B) 2. That being said, the following solutions were found n(A) = 3 n(B) = 5 - Therefore, he wrote three projects without producing them. confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): The book, on p. 83, it says that he wrote and produced 2 projects. However, in your question, it says he wrote and produced three. In your given solution it keeps with the book, and then you later mention the intersecting region would have 3 elements. Am I reading something wrong, or has a minor discrepancy been discovered? ------------------------------------------------ Self-critique Rating:
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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.** " 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: - This one took longer than I anticipated. Another “can’t see the forest for the trees” instances. Regardless, I drew three circles to represent fat, male, and red. a. Fat - 37 b. Red - 5 c. Male - 18 d. Fat, not male - 2 e. brown, not fat - 26 f. red, fat - 11 At first I was attempting to calculate…when I realized I could simply match the items from the problem in the book to the corresponding regions in the diagram. 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.** " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!