course mth151 Ekҽ侴ti assignment #002 002. `Query 2 College Algebra 10-28-2007
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17:17:36 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 --> true all of C is a subset of U confidence assessment: 2
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17:17:53 ** It's true because all elements of C are in the universal set, and because there are elements of U that aren't in C. You have to have both conditions, since a proper subset cannot be identical to other set. **
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RESPONSE --> okay self critique assessment: 2
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17:19:01 Query 2.2.30 phi s D
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RESPONSE --> statement is false phi is not a subset of D confidence assessment: 2
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17:19:42 ** 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 --> okay self critique assessment: 2
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17:20:35 2.2.33 D not s B Is the statement true or false and why?
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RESPONSE --> True, not all of D is part of B. confidence assessment: 2
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17:20:54 ** D is a subset of B if every element of D is an element of B-i.e., if D doesn't contain anything that B doesn't also contain. The statement says that D is not a subset of B. This will be so if D contains at least one element that B doesn't. **
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RESPONSE --> okay self critique assessment: 2
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17:21:56 2.2.36 there are exactly 31 subsets of B
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RESPONSE --> false, there are five twenty five subsets of B confidence assessment: 1
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17:22:30 ** 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 was close but i used the wrong forumla self critique assessment: 2
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17:23:36 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 --> false there are 49 subset of 7 confidence assessment: 1
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17:24:35 ** 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 --> again the wrong forumla was used. self critique assessment: 1
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17:25:50 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 complement is (1,3,4,6,8) confidence assessment: 2
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17:26:00 ** the complement is {1,3,4,6,8}, the set of all elements in U that aren't in the given set. **
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RESPONSE --> okay self critique assessment: 2
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17:27:27 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 --> i am not sure of my answer, but i came to the conclusion of 15 confidence assessment: 13
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17:28:04 ** The answer here would consist of a list of all 3-element subsets: {a,b,c}, {a,b,d}, {a,b,e}, {a,c,d} etc. There are ten such subsets. Using a,b,c,d,e to stand for the names, we can list them in alphabetical order: {a,b,c), {a,b,d}, {a,b,e}, {a,c,d}, {a,c,e}, {a,d,e|, {b,c,d}, {b,c,e}, {b,d,e}, {c, d, e}**
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RESPONSE --> i was way off base, with the working of the problem self critique assessment: 1