course Mth 151 ZTKஂɶRassignment #002
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17:12:27 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 --> It is true because all the elements in C is in U. Just because all the elements of U is not showing the dots indicate they are there. confidence assessment: 3
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17:13:45 ** 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 --> I forgot about the other condition of a proper subset of there has to be elements in U that are not in C. self critique assessment: 2
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17:14:38 Query 2.2.30 phi s D
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RESPONSE --> What does this mean? confidence assessment: 0
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17:17:45 ** 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 understand now good thing I did my text homework before this. self critique assessment: 2
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17:20:51 2.2.33 D not s B Is the statement true or false and why?
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RESPONSE --> D is not a subset of B because all the elements of D is not in C. confidence assessment: 3
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17:23:05 ** 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 understand this.l self critique assessment: 1
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17:25:12 2.2.36 there are exactly 31 subsets of B
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RESPONSE --> This is false it has 32 subsets because there are 5 elements. If it was saying there were 31 proper subsets then that would be correct. confidence assessment: 3
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17:25:39 ** 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 --> Exactly! self critique assessment: 1
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17:28:12 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 --> This is true because there are 128 subsets and to find how many proper subsets there are then that would be 128 - 1 which would equal 127. confidence assessment: 3
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17:29:34 ** 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 it! self critique assessment: 1
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17:31:51 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 of the set would be {1,3,4,6,8}. These are the numbers left over which is the complement. confidence assessment: 3
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17:32:12 ** 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 --> Yeah! self critique assessment: 1
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17:34:24 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 had a hard time with this one. The book said 10 but I don't understand this. confidence assessment: 0
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17:35:38 ** 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 don't know why I am so confused with this problem. self critique assessment: 0
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17:44:48 Query 2.1.12 counting #'s 4 to 14 List the elements of the set.
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RESPONSE --> {5,6,7,8,9,10,11,12,13} confidence assessment: 3
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17:45:40 **A list of the elements would just be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. **
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RESPONSE --> But it says between 4 and 14 why would you include 4 and 14? self critique assessment: 1
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17:47:00 query 2.1.24 set builder for set of presidents between LBJ and Clinton
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RESPONSE --> {Nixon, Ford, Carter, Reagan, Bush, Clinton} confidence assessment: 3
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17:50:15 ** 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 --> So you don't actually list them? and when asking for set notation do have to put the x l x? self critique assessment: 0
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17:51:35 2.1.40 finite or infinite: set of rat #'s 0 to 1
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RESPONSE --> {.5} confidence assessment: 3
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17:54:07 ** 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 --> I forgot to put that it was finite. So does it go on forever or not. I would say that it doesn't since it is between 2 numbers. self critique assessment: 0
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17:58:44 2.1.48 n(A), A={x|x is a U.S. senator} What is n(A) and why?
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RESPONSE --> It would be 100 because there are 100 U.S. Senators. n(A) represents cardinality of the set which means how many elements are there in the set. confidence assessment: 3
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17:59:06 ** n(A) stands for the number of elements in the set--in this case for the number of senators. There are 100, 2 from each State. So n(A) = 100. **
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RESPONSE --> Great! self critique assessment: 2
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18:01:38 query 2.1.54 {x|x is neagtive number}
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RESPONSE --> It would be well defined because it can be defined and not opinion or unmeasurable. confidence assessment: 3
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18:02:20 ** 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 --> Yes! self critique assessment: 2
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18:03:08 2.1.72 true or false 2 not subset of {7,6,5,4}
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RESPONSE --> It is true because 2 is not an element. confidence assessment: 3
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18:04:15 ** 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 --> I understand why. self critique assessment: 1
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18:06:39 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 --> I had true in my homework because the question was is 8 an element of B and it is. This question however is false because every element of C is not in B. confidence assessment: 3
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18:06:52 ** Specifically it's false because the element 12 is in C but not in B. **
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RESPONSE --> O.K. self critique assessment: 1
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