#$&* course Mth 151 9/14/14 5:03pm 001. `Query 1
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: {4, 5,6,7,8,9,10,11,12,13,14} confidence rating #$&*: 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a**For the set of counting numbers from 4 through 14 the list of the elements would be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. To indicate the set of these element using a list format we would write the set as {4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14}. If we are asked for the set of counting numbers between 4 and 14 we would write the set as {5, 6, 7, 8, 9, 10, 11, 12, 13}. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qquery 2.1.24 listing for set of presidents after Nixon and before Obama (formerly between LBJ and Clinton)
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: {Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Reagan, George Bush, Bill Clinton} confidence rating #$&*: 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The solution given here is for presidents between Johnson and Clinton. A listing would be {}{}{ Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Regan, George HW Bush}.{}{}Set-builder notation is {x|x is a president who served between Lyndon Johnson and William Clinton} x is a variable and the condition 'x is a president who served between Lyndon Johnson and William Clinton' tells you what possible things the variable can be. COMMON ERROR: It's incorrect to say {x | x is the set of presidents who served between Johnson and Clinton}. x is a president, not a set of presidents. Should be {x|x is a president who served between Lyndon Johnson and William Clinton} ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q2.1.44 finite or infinite: set of rat #'s 0 to 1
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The amount of rational numbers between 0 to 1 is an infinite and this is part of one sub set {1/2, 1/3, ¼, 1/5, 1/6, 1/7, 1/8….} confidence rating #$&*: 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q2.1.48 n(A), A={x|x is a U.S. senator} What is n(A) and why?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: n(A) is the number in the set and for this problem it is the number of senators. n(A)=100 because there are 2 senators for each of the 50 states so 100. 50(2)=100 confidence rating #$&*:: 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** n(A) stands for the number of elements in the set--in this case for the number of senators. There are 100, 2 from each State. So n(A) = 100. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qquery Is {x|x is negative number} well-defined?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Yes it means that all the possible values of x such that x are negative numbers. And it is possible to tell or define if something is in this set. confidence rating #$&*: 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!
#$&* course Mth151 9/14/14 735pm 002. Representing Sets
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Given Solution: The circles would appear and be labeled as below: The letters a, c and f go in the overlapping region, which we called Region I. The remaining letters in the first collection are b, d, and e, and they go in the part of the first circle that does not include the overlapping region, which we called Region II. The letters g and k go in the part of the second circle that does not include the overlapping region (Region III). There are no letters in Region IV. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q002. Suppose that we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair and bright eyes. Draw two circles, one representing the dark-haired people and the other representing the bright-eyed people. Represent the dark-haired people without bright eyes by writing this number in the part of the first circle that doesn't include the overlap (region II). Represent the number of bright-eyed people without dark hair by writing this number in the part of the second circle that doesn't include the overlap (region III). Write the appropriate number in the overlap (region I). How many people are included in the first circle, and how many in the second? How many people are included in both circles? How many of the 35 people are not included in either circle? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: In the first circle or region II there are 12 people. In the second circle or region III there are 7 people. In the first circle or Region II 12, second circle or Region III or 7 and the overlap Region I 8 so 12+7+8=27. Region IV has 8 because there are 8 people who do not fit into the first circle or the second circle and when added to 27+8=35. . confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: These numbers are represented in the circles below. • A number on the boundary of a circle indicates the total number in that circle, so the figure represents 20 individuals in circle A and 15 in circle B. The number 35 on the boundary of the entire figure represents the total number of individuals in the room, which in this case is 35. • A number inside one of the regions I, II, III, IV represents the number in that region. The 8 having both dark hair and bright eyes will occupy the overlap between the circles (region I). Of the 15 people with bright eyes, 8 also have dark hair so the other 7 do not have dark hair, and this number will be represented by the part of the second circle that doesn't include the overlap (region III). This is indicated by the number 7 inside region III in the figure below. Of the 20 dark-haired people in the preceding example, 8 also have bright eyes. This leaves 12 dark-haired people for that part of the circle that doesn't include the overlap (region II). We have accounted for 12 + 8 + 7 = 27 people. This leaves 35-27 = 8 people who are not included in either of the circles. The number 8 can be written outside the two circles (region IV) to indicate the 8 people who have neither dark hair nor bright eyes, as is indicated by the number 8 in region IV in the figure below: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q003. Suppose there are 200 people in a hall, 140 having dark hair, 90 having short hair and 50 having hair which is neither dark nor short. Sketch a diagram like the ones above, specify how many people are in each of the four regions and describe the people in each region. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: In first circle or region II 60 in second circle or region III 10 and in the overlap or region I 80 and region IV 50. That means region II + region III +region I which is 60+10+80=150 add region IV 50 to it and you have 200 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q003. Suppose there are 200 people in a hall, 140 having dark hair, 90 having short hair and 50 having hair which is neither dark nor short. Sketch a diagram like the ones above, specify how many people are in each of the four regions and describe the people in each region. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: In first circle or region II 60 in second circle or region III 10 and in the overlap or region I 80 and region IV 50. That means region II + region III +region I which is 60+10+80=150 add region IV 50 to it and you have 200 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!