course math 151 I did 3 and 4 but they just have the bottom responces ---------> I guess I will do them over. Please tell me when I can take my first test or what more I need to do inorder to take it! I want to take 2 or 3 with in the first 2 weeks of feb! Thank you so much this is much easier the second time around!
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08:01:49 2.2.24 U={a,b,...,g}, A={a,e}, B={a,b,e,f,g}, C={b,f,g}, D={d,e} Is C ps U? Is the statement true or false and why?
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RESPONSE --> The answer to 2.2.24 is true because U=a through g and d,e are the intersections of that.
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08:03:20 Query 2.2.30 phi s D
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. I understand this question Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.
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08:04:10 Query 2.2.30 phi s D
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RESPONSE --> I'm not sure how to answer 2.2.30 because all my screen says is phi is D.
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08:09:40 ** Note that You should be responding to problem 2.2.30 from the homework you worked out on paper. The shorthand notation is for my reference and won't always make sense to you. For clarification, though, the symbol for the empty set is the Greek letter phi. One set is a subset of another if every element of that set is in the other. To show that a set isn't a subset of another you have to show something in that set that isn't in the other. There's nothing in the empty set so you can never do this--you can never show that it has something the other set doesn't. So you can never say that the empty set isn't a subset of another set. Thus the empty set is a subset of any given set, and in particular it's a subset of D. ALTERNATIVE ANSWER: As the text tells you, the empty set is a subset of every set. ANOTHER ALTERNATIVE Every element of the empty set is in D because there is no element in the empty set available to lie outside of D. ONE MORE ALTERNATIVE: The empty set is a subset of every set. Any element in an empty set is in any set, since there's nothing in the empty set to contradict that statement. **
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RESPONSE --> I do understand now that I realize I was responding to the text. And knowing that the symbol of /0 is phi, then # 30. on page 61 makes sense.
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08:22:27 2.2.33 D not s B Is the statement true or false and why?
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RESPONSE --> The answer to 2.2.33 is true because d is not a subset belonging to set B.
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08:24:51 2.2.36 there are exactly 31 subsets of B
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. I understand this question. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.
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08:27:14 2.2.36 there are exactly 31 subsets of B
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RESPONSE --> The answer to 2.2.36 is false, because there are 25 subsets to this problem.
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08:31:04 ** If a set has n elements then is has 2^n subsets, all but one of which are proper subsets. B has 5 elements so it has 2^5 = 32 subsets. So the statement is false. There are exactly 31 proper subsets of B, but there are 32 subsets of B. **
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RESPONSE --> I responded false, but I did not understand why it was false.
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08:34:09 Query 2.2.40 there are exactly 127 proper subsets of U Is the statement true or false and why?
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RESPONSE --> The answer to 2.2.40 is false because there are 2^ n or 7x7=49.
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08:39:31 ** The set is not a proper subset of itself, and the set itself is contained in the 2^n = 2^7 = 128 subsets of this 7-element set. This leaves 128-1 = 127 proper subsets. **
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RESPONSE --> I got the answer correct, and I finally undferstand that it is 2 to the seventh power. Yeah!!!!!!!
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08:44:04 Query 2.2.48 U={1,2,...,10}, complement of {2,5,7,9,10} What is the complement of the given set?
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RESPONSE --> The answer to 2.2.48 is the complement is 1,3,4,6,8.
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08:46:00 query 2.2.63 in how many ways can 3 of the five people A, B, C, D, E gather in a suite?
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. I get this idea, and got the question correct. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.
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08:46:41 query 2.2.63 in how many ways can 3 of the five people A, B, C, D, E gather in a suite?
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RESPONSE --> The answer to 2.2.63 is 10 ways.
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KŔC惕a assignment #003 gm{`z{ Liberal Arts Mathematics I 01-28-2006
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08:59:40 Query 2.3.15 (Y ^ Z')U X, univ={a,..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 --> The answer to 2.3.15 is Y to the Z power times U times X. So, abc to the bcdef power .
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09:02:24 Give the intersection of the two sets Y and Z'
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. I did not get this question correct. I would like to be able to go back to see the original query, because now I do not remember what the sets are to Y and Z. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.
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09:03:55 Give the intersection of the two sets Y and Z'
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RESPONSE --> The intersection of two sets Y and Z are: {xIx E Y and E Z}
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09:18:59 Query 2.3.30 describe in words (A ^ B' ) U (B ^ A')
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Now I'm cofused because you have an answer in the left box from about 2 questions ago, and underneath it is Query 2.3.30?????? Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.
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09:27:06 Query 2.3.30 describe in words (A ^ B' ) U (B ^ A')
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RESPONSE --> The answer to query 2.3.30 is The set of elements that are in A^B are in the set of elements in B^A.
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09:29:17 ** 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 --> I got that wrong.I like the student solution with instructor comment as a description that I understand better.
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09:31:25 2.3.51 always or not always true: n(A U B) = n(A)+n(B)
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RESPONSE --> 2.3.51 Answer is not always true because it could be either n(A) or n(B) not added together.
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09:32:11 Query 2.3.60 X = {1,3,5}, Y = {1,2,3}. Find (X ^ Y)' and X' U Y'.
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. I unsderstand this. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.
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10:07:06 ** 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 --> I din't even answer this one, I left my computer for a few minutes, and the screen went on a blank screen saver, then this answer came up.
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10:17:35 2.3.72 A = {3,6,9,12}, B = {6,8}.
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RESPONSE --> The answer to 2.3.72 is A x B= {(3,6), (3,8), (6,6), (6,8), (9,6), (9, 8), (12,6), (12,8)} and B x A= { (6,3), (6,6), (6,9), (6,12), (8,3), (8,6), (8,9), (8,12)}.
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10:18:21 2.3.84 Shade A U B
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. I understand this good. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.
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10:18:56 ** 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 --> I didn't have a question to go along with this explanation??????
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10:23:16 Query 2.3.100 Shade (A' ^ B) ^ C
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RESPONSE --> Answer to 2.3.100 is on paper, I didn't see a way to put it on the computer.
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10:31:17 ** 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 --> According to the explanation, I shaded my paprer correctly.
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10:35:34 Describe the shading of the set (A ^ B)' U C.
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RESPONSE --> It would not include where A meets C, or where B meets C, but includes all the rest of the three circles.
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11:02:06 ** 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 --> This is how I pictured the answer.
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11:13:31 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 --> Answer to query 2.3.114 is The region in color is in set A, and is not B, or it is not in C. There are no subsets, the union is the portion outside of A and outside of B, and outside of C, and the intersections are unshaded. So, A U B` U C`.
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11:16:00 ** 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 --> Please explain to me what the ^ symbol means???
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assignment #001 gm{`z{ Liberal Arts Mathematics I 01-27-2006
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13:29:42 Query 2.1.12 counting #'s 4 to 14 List the elements of the set.
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RESPONSE --> the answer is {4,5,6,7,8,9,10,11,12,13,14}
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13:31:10 query 2.1.24 set builder for set of presidents between LBJ and Clinton
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. I got this question correct.
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13:34:09 query 2.1.24 set builder for set of presidents between LBJ and Clinton
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RESPONSE --> The answer is {Richard Nixon, Geerald Ford, Jimmy Carter, Ronald Reagan, and George Bush (Sr.)}
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13:37:37 ** Set-builder notation is {x|x is a president who served between Lyndon Johnson and William Clinton} x is a variable and the condition 'x is a president who served between Lyndon Johnson and William Clinton' tells you what possible things the variable can be. COMMON ERROR: It's incorrect to say {x | x is the set of presidents who served between Johnson and Clinton}. x is a president, not a set of presidents. Should be {x|x is a president who served between Lyndon Johnson and William Clinton} **
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RESPONSE --> I got that one wrong, as I listed the names instesd of doing a set-builder notation. I do understand the set-builder notation should be {xIx is the president who served between Lyndon Johnson and William Clinton}
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13:38:16 2.1.40 finite or infinite: set of rat #'s 0 to 1
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RESPONSE --> Answer to 2.1.40 is Finite
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13:42:46 ** Rational numbers have form p/q, where p and q are integers. Numbers like 5/8, 57/31, -3/5, -57843/7843, etc. The subset {1/2, 1/3, 1/4, 1/5, ... } is just by itself an infinite set of rational numbers between 0 and 1. Then you have things like 348/937, and 39827389871 / 4982743789, and a whole infinite bunch of others. There are thus infinitely many rational numbers in any interval of the real line. COMMON MISCONCEPTION: finite, because it doesn't go on forever Rational numbers have form p/q, where p and q are integers. Numbers like 5/8, 57/31, -3/5, -57843/7843, etc. Not all of these lie between 0 and 1, of course. **
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RESPONSE --> While I see your point, the set of numbers between 0 and 1 do have a stopping point- 1.
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13:53:47 2.1.48 n(A), A={x|x is a U.S. senator} What is n(A) and why?
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RESPONSE --> Answer to 2.1 48 is 100 active, because there are 2 for each of the 50 states. This answer would not include the past senators.
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13:55:04 query 2.1.54 {x|x is neagtive number}
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. OK! Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. OK !
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14:02:42 query 2.1.54 {x|x is neagtive number}
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RESPONSE --> Answer to xIx is a negative number is not well defined because is does not specify whether or not the answer needs to be a counting rational number. Answer is: {-1,-2,-3,-4........}
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14:03:12 ** This notation means all possible values of x such that x is a negative number. The question is whether the set is well-defined or not. It is in fact well-defined because there is a definite way to decide whether a given object is an element of the set, because there is a definite way to determine whether an object is a negative number or not. ALTERNATIVE ANSWER: The set is well-defined because you have a criterion by which you can definitely decide whether something is or is not in the set. **
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RESPONSE -->
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14:03:41 ** This notation means all possible values of x such that x is a negative number. The question is whether the set is well-defined or not. It is in fact well-defined because there is a definite way to decide whether a given object is an element of the set, because there is a definite way to determine whether an object is a negative number or not. ALTERNATIVE ANSWER: The set is well-defined because you have a criterion by which you can definitely decide whether something is or is not in the set. **
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RESPONSE --> I understand now thw it is well defined because it tells exactly what it wants!
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14:06:28 2.1.72 true or false 2 not subset of {7,6,5,4}
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RESPONSE --> Answer to 2.1.72 is True
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14:07:54 ** The statement is that 2 is not a subset. The statement is true because 2 isn't even a set, it's just a number. {2} is a set and could be a subset of something. 2 is just a number; it isn't a set so it can't be a subset of anything. The usual answer is that 2 isn't a subset because 2 isn't in the set. However that's not the correct reason. The correct reason is that 2 isn't a set and a subset must be a set. COMMON MISCONCEPTION: the statement says that 2 is not a subset, not that it is not an element of the set. So the reason it's not a subset is that 2 isn't a set at all, so it can't be a subset of anything. **
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RESPONSE --> That is correct, because 2 is not a subset if it's not even a set.
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14:12:59 2.1.84 C={4,10,12}, B={2,4,8,10} Is it true or false that every element of C is also an element of B?
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RESPONSE --> Answer to 2.1.84 is False, because not all elements are contained in B.
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Bottom responces: yޑxꚠ_m踃zܗ Student Name: assignment #005 001. Rates"