course mth151 N¿ÇDÉØίÃ׆¯x}ná™xpy•MÞ•assignment #003
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16:34:55 Query 2.3.15 This might differ from the problem as given in the text, but you should be able to answer it for the given sets: universal set U = {a,b, c,…,g}, X={a,c,e,g}, Y = {a,b,c}, Z = {b, ..., f} What is the set (Y ^ Z')U X?
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RESPONSE --> y^z=(a,b,c,d,e,f,g) and the union of X (y^z)U x=(c,e) confidence assessment: 2
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16:36:02 **Z' = {a,g}, the set of all elements of the universal set not in Z. Y ^ Z' = {a}, since a is the only element common to both Y and Z'. So (Y ^ Z') U X = {a, c, e, g}, the set of all elements which lie in at least one of the sets (Y ^ Z') U X. **
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RESPONSE --> a little off with y^z. but i am pretty confident with the process. self critique assessment: 2
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16:37:46 Give the intersection of the two sets Y and Z'
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RESPONSE --> i didn't write down the given information to first problem and didn't write down the example from the text. confidence assessment: 0
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16:38:05 **Z' = {a,g}, the set of all elements of the universal set not in Z. Y ^ Z' = {a}, since a is the only element common to both Y and Z'.**
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RESPONSE --> okay self critique assessment: 0
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16:40:32 Query 2.3.32 (formerly 2.3.30). This was not assigned, but you answered a series of similar questions and should be able to give a reasonable answer to this one: Describe in words (A ^ B' ) U (B ^ A')
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RESPONSE --> a set of elements that are with A and the oppisite of B,which form the union of B and the oppisite of A. confidence assessment: 2
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16:40:55 ** a description, not using a lot of set-theoretic terms, of (A ^ B' ) U (B ^ A') would be, all the elements that are in A and not in B, or that are not in A and are in B Or you might want to say something like 'elements which are in A but not B OR which are in B but not A'. STUDENT SOLUTION WITH INSTRUCTOR COMMENT:everything that is in set A and not in set B or everything that is in set B and is not in set A. INSTRUCTOR COMMENT: I'd avoid the use of 'everything' unless the word is necessary to the description. Otherwise it's likely to be misleading. **
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RESPONSE --> okay self critique assessment: 2
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16:44:15 2.3.53 (formerly 2.3.51) Is it always or not always true that n(A U B) = n(A)+n(B)? This was not among the assigned questions but having completed the assignment you should be able to answer this.
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RESPONSE --> this would be false. n(A u B) is the point were the to groups meet. n(A)+n(B) may not always add up to a correct solution confidence assessment: 2
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16:44:37 ** This conclusion is contradicted by many examples, including the one of the dark-haired and bright-eyed people in the q_a_. Basically n(A U B) isn't equal to n(A) + n(B) if there are some elements which are in both sets--i.e., in the intersection. } MORE DETAIL: The statement can be either true or false, depending on the sets A and B; it is not always true. The statement n(A U B) = n(A)+n(B) means that the number of elements in A U B is equal to the sum of the number of elements in A and the number of elements in B. The statement would be true for A = { c, f } and B = { a, g, h} because A U B would be { a, c, f, g, h} so n(A U B) = 5, and n(A) + n(B) = 2 + 3 = 5. The statement would not be true for A = { c, f, g } and B = { a, g, h} because A U B would be the same as before so n(AUB) = 5, while n(A) + n(B) = 3 + 3 = 6. The precise condition for which the statement is true is that A and B have nothing in common. In that case n(A U B) = n(A) + n(B). A more precise mathematical way to state this is to say that n(A U B) = n(A) + n(B) if and only if the intersection A ^ B of the two sets is empty. **
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RESPONSE --> okay self critique assessment: 2
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16:46:02 Query 2.3.60 X = {1,3,5}, Y = {1,2,3}. Find (X ^ Y)' and X' U Y'.
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RESPONSE --> x^y=(1,3) X' U Y'= (4) confidence assessment: 2
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16:46:38 ** X ^ Y = {1,3} so (X ^ Y) ' = {1,3}' = {2, 4, 5}. (X ' U Y ' ) = {2, 4} U {4, 5} = {2, 4, 5} The two resulting sets are equal so a reasonable conjecture would be that (X ^ Y)' = X' U Y'. **
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RESPONSE --> okay self critique assessment: 1
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16:50:35 2.3.72 A = {3,6,9,12}, B = {6,8}.
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RESPONSE --> A x B = (3,6),(3,8) B xA =(6,3),(6,6)(6,9),(6,12),(8,3),(8,6),(8,9),(8,12) confidence assessment: 2
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16:50:54 ** (A X B) = {(3,6),(3,8),(6,6),(6,8),(9,6),(9,8),(12,6), (12,8)} (B X A) = (6,3),(6,6),(6,9),(6,12),(8,3),(8,6),(8,9),(8,12)} How is n(A x B) related to n(A) and n(B)? n(S) stands for the number of elements in the set S, i.e., its cardinality. n(A x B) = n(A) * n(B) **
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RESPONSE --> okay self critique assessment: 2
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16:51:57 2.3.84 Shade A U B
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RESPONSE --> the section which were A and B interect would be shaded. confidence assessment: 1
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16:52:11 ** everything in A and everything in B would be shaded. The rest of the universal set (the region outside A and B but still in the rectangle) wouldn't be. **
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RESPONSE --> okay self critique assessment: 1
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16:52:56 Query 2.3.100 Shade (A' ^ B) ^ C
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RESPONSE --> B and C would be shaded and A would not be confidence assessment: 2
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16:53:09 ** you would have to shade every region that lies outside of A and also inside B and also inside C. This would be the single region in the overlap of B and C but not including any part of A. Another way to put it: the region common to B and C, but not including any of A **
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RESPONSE --> okay self critique assessment: 1
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16:54:10 Query 2.3.108. Describe the shading of the set (A ^ B)' U C.
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RESPONSE --> C would be shaded and A and B would not confidence assessment: 2
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16:54:25 ** All of C would be shaded because we have a union with C, which will include all of C. Every region outside A ^ B would also be shaded. A ^ B is the 'overlap' region where A and B meet, and only this 'overlap' would not be part of (A ^ B) '. The 'large' parts of A and B, as well as everything outside of A and B, would therefore be shaded. Combining this with the shading of C the only the part of the diagram not shaded would be that part of the 'overlap' of A and B which is not part of C. **
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RESPONSE --> okay self critique assessment: 2
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16:55:40 2.3.114 Largest area of A shaded (sets A,B,C). Write a description using A, B, C, subset, union, intersection symbols, ', - for the shaded region.
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RESPONSE --> Shade list of A only confidence assessment: 1
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16:55:42 2.3.114 Largest area of A shaded (sets A,B,C). Write a description using A, B, C, subset, union, intersection symbols, ', - for the shaded region.
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RESPONSE --> confidence assessment:
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16:56:16 ** Student Answer and Instructor Response: (B'^C')^A Instructor Response: Good. Another alternative would be A - (B U C ), and others are mentioned below. COMMON ERROR: A ^ (B' U C') INSTRUCTOR COMMENT: This is close but A ^ (B' U C') would contain all of B ^ C, including a part that's not shaded. A ^ (B U C)' would be one correct answer. **
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RESPONSE --> i had the wrong thought when i was reading the guestion self critique assessment: 2
Deconstruct the given solution and explain in detail what you do and do not understand about every part.. &#
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