course Mth 151 ????n??assignment #002
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16:21:14 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 because b,f and g are in U. confidence assessment: 3
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16:24:02 ** 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 --> So proper subsets are having just parts of the universal in them and not all as would be a subset self critique assessment: 3
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16:26:40 Query 2.2.30 phi s D
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RESPONSE --> true because it is impoosible to find any elements of empty set that are not also in D. confidence assessment: 3
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16:28:22 ** 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 --> My thoughts exactly. So type phi for empty? Since phi is an element it can also be a set. self critique assessment: 2
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16:30:39 01-17-2007 16:30:39 2.2.33 D not s B Is the statement true or false and why?
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NOTES -------> true because D does not have all the elements that B has. This could be proper set but not a subset.
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16:30:44 2.2.33 D not s B Is the statement true or false and why?
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RESPONSE --> confidence assessment: 3
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16:32:47 ** 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 --> I am not sure that I got the answer right. d and e are in B but not all of them so it should be true self critique assessment: 2
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16:34:27 2.2.36 there are exactly 31 subsets of B
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RESPONSE --> False. There are 32 subsets in B and there are 31 proper subsets in B confidence assessment: 3
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16:35:04 ** 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 understand this very well self critique assessment: 3
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16:36:12 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 --> True. There are 128 subsets in U so then there would be 127 proper subsets. confidence assessment: 3
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16:36:55 ** 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 understand self critique assessment: 3
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16:41:11 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 --> I think you are asking us question 50 instead of 48. 48) whole number less than 4 are 1 and 3. There are three elements so there would be 4 subsets and 3 proper subsets. 0 counts for an even number right?
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16:41:38 ** 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 --> so to compliment the set means to complete it. self critique assessment: 3
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16:42:20 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 --> abc, abd, abe, bcd, bce, cde, acd, ace, ade, bde (10 ways) confidence assessment: 3
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16:42:51 ** 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 --> it is just a process of rearranging the letters. self critique assessment: 3
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