course Mth 151 Í…‚æòﬧ‰Á|Ød›pçï§}œÙ}œLàòÐassignment #002
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22:18:43 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 characters in C are also found in U. confidence assessment: 3
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22:18:58 ** 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 --> self critique assessment: 2
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22:26:56 Query 2.2.30 phi s D
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RESPONSE --> True. Since there are no elements in phi, then there aren't any elements in phi that are not in D. confidence assessment: 3
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22:27:59 ** 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 answered with the first alternative answer. self critique assessment: 3
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22:29:27 2.2.33 D not s B Is the statement true or false and why?
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RESPONSE --> True. Every element in D is not found in B. In this particular case its 'd'. confidence assessment: 3
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22:47:59 2.2.36 there are exactly 31 subsets of B
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RESPONSE --> False. There are 31 proper subsets of B (2^n - 1 where n= the number of elements in the subset). Since this did not specifically state the number of proper subsets, the actual number of subsets would be 2^5=32. confidence assessment: 2
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22:48:15 ** 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 --> Right on! self critique assessment: 3
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22:49:58 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 7 elements to this subset and since the question is asking for proper subsets, then the following equation would be used: 2^7 - 1 = 127 confidence assessment: 3
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22:57:28 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 am confused. The answer to Question 2.2.48 in the book is 4 = number of subsets (since there were two numbers in the subset (1 and 3). 3 = number of proper subsets. As far as the question 'what is the complement of the given set?', the answer is U' since there are elements of the second subset that do not appear in U. confidence assessment: 2
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22:58:47 ** 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 --> Ok, I was confused with the answer. I didn't realize that you wanted me to list out the numbers that were in U but not in the second set. That's why I just answered U'. self critique assessment: 2
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23:04:36 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 --> 10 confidence assessment: 2
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23:04:55 ** 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 --> self critique assessment: 3
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