#$&* course mth 151 1/17/12, 7:48 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: All numbers from 4 to 14. (4,5,6,7,8,9,10,11,12,13,14) confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a**A list of the elements would just be 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating: ok ********************************************* Question: `qquery 2.1.24 listing for set of presidents between LBJ and Clinton
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The set of presidents between Lyndon B. Johnson and Bill Clinton. Well for this you have to know the presidents. Then do a list from Johnson to Clinton. *** which is {x|x confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** A listing would be {}{}{Lyndon Johnson, Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Regan, George HW Bush, William Clinton}.{}{}Set-builder notation is {x|x is a president who served between Lyndon Johnson and William Clinton} x is a variable and the condition 'x is a president who served between Lyndon Johnson and William Clinton' tells you what possible things the variable can be. COMMON ERROR: It's incorrect to say {x | x is the set of presidents who served between Johnson and Clinton}. x is a president, not a set of presidents. Should be {x|x is a president who served between Lyndon Johnson and William Clinton} ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I knew that I had to do a list of all between the given presidents. Then after reading the solution found the equation that is used. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q2.1.40 finite or infinite: set of rat #'s 0 to 1
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Finite- is numbers that end. Infinite- When a set is so large that a cardinal number cannot be found. confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): Infinite is ones that are easy to describe. Like the ¼, ½… .25 etc. While the finite would be something that does not stop going??????????????? ------------------------------------------------ Self-critique Rating: 2
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: A is the elements in a sat. such as (1,2,3,4,5). This is asking for the number of senators. Which is 2 a state. Which is 50 states. 2*50= 100 senators. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** n(A) stands for the number of elements in the set--in this case for the number of senators. There are 100, 2 from each State. So n(A) = 100. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating: ok ********************************************* Question: `qquery 2.1.54 {x|x is neagtive number}
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: We are not given a set, so it can be any number of possibilities. **** It is well defined since there is not a certain set listed to be wrong about. confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ok ------------------------------------------------ Self-critique Rating: ok ********************************************* Question: `q2.1.74 (formerly 2.1.72) This was not assigned, but you should be able to answer based on your work on similar problems: It is or is it not true that 2 is not not subset of {7,6,5,4}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Correct 2 is not a subset. 2 is not in the list of numbers. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The statement is that 2 is not a subset. The statement is true because 2 isn't even a set, it's just a number. {2} is a set and could be a subset of something. 2 is just a number; it isn't a set so it can't be a subset of anything. The usual answer is that 2 isn't a subset because 2 isn't in the set. However that's not the correct reason. The correct reason is that 2 isn't a set and a subset must be a set. COMMON MISCONCEPTION: the statement says that 2 is not a subset, not that it is not an element of the set. So the reason it's not a subset is that 2 isn't a set at all, so it can't be a subset of anything. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: ok ********************************************* Question: `q2.1.86 (formerly 2.1.84). This was not assigned but you did answer several questions related to the sets C={4,10,12}, B={2,4,8,10}, and should be able to answer this. Is it true or false that every element of C is also an element of B? Be sure to include your reasoning.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: False. 12 is not part of the set of b. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** Specifically it's false because the element 12 is in C but not in B. ** " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q2.1.86 (formerly 2.1.84). This was not assigned but you did answer several questions related to the sets C={4,10,12}, B={2,4,8,10}, and should be able to answer this. Is it true or false that every element of C is also an element of B? Be sure to include your reasoning.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: False. 12 is not part of the set of b. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** Specifically it's false because the element 12 is in C but not in B. ** " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&! ********************************************* Question: `q2.1.86 (formerly 2.1.84). This was not assigned but you did answer several questions related to the sets C={4,10,12}, B={2,4,8,10}, and should be able to answer this. Is it true or false that every element of C is also an element of B? Be sure to include your reasoning.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: False. 12 is not part of the set of b. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** Specifically it's false because the element 12 is in C but not in B. ** " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!