#$&* course Mth 151 I have a feeling I did this one already, but I figure I would submit it just in case. Sorry for any confusion. Question: `q2.2.24 U={a,b,...,g}, A={a,e}, B={a,b,e,f,g}, C={b,f,g}, D={d,e} Is C ps U?
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I am not sure what you meant by ps in the question Is C ps U? I understand that the elements in C are in the U set and that not all the elements that are in the U set are in the C set.
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I understand that I should of looked at the question #30 in the 2.2 problem. I think I understand that the answer should be false because an empty set has nothing in and the “D” set has two. Is this correct????
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I do not like these questions. Just making a statement, I hope I am explaining my answering correctly. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q2.2.36 there are exactly 31 subsets of B YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: That is true. The reason why it is true is the following: In the set “B” you have {a, b, e, f, g} and in this set you five elements in it. You in order to find the proper subsets you take 2 and put the elements and make them a power of the 2. For example: 2^5 which gives you 32 subsets then you subtract 1 from the 32 subsets giving you 31 proper subsets. confidence rating #$&*:: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I do not like this, as you can see in my solution I understand the basics. I am just getting things mixed up on what is actually being asked.
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I think what you put is what I put down. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qQuery 2.2.48 U={1,2,...,10}, complement of {2,5,7,9,10} What is the complement of the given set? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The complement of the given set is all the numbers that are in the U set, but not in the other set giving you a set of {1, 3, 4, 6, 8} confidence rating #$&*:: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** the complement is {1,3,4,6,8}, the set of all elements in U that aren't in the given set. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I finally got one right and fully understand it. Self-critique Rating: ********************************************* Question: `qquery 2.2.63 in how many ways can 3 of the five people A, B, C, D, E gather in a suite? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: {a, b, c}; {a, d, e}; {b, c, d}; {b, e, a}; {c, d, e}; {c, a, b}; {d, e, a}, {d, b, c}, {e, a, c}; {e, b, d} You will have 10 ways that you can get 3 of the five people to gather in a suite. confidence rating #$&*:: ********************************************* Question: `qquery 2.2.63 in how many ways can 3 of the five people A, B, C, D, E gather in a suite? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: {a, b, c}; {a, d, e}; {b, c, d}; {b, e, a}; {c, d, e}; {c, a, b}; {d, e, a}, {d, b, c}, {e, a, c}; {e, b, d} You will have 10 ways that you can get 3 of the five people to gather in a suite. confidence rating #$&*:: #(*!