#$&* course Mth 151 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} Counting numbers are whole numbers. The set includes counting numbers 4 to 14, not numbers between 4 and 14. Therefore, the set would include 4, 14, and every whole number in between. I have wrote them out in the “Listing Method” because it said to “list” the elements. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `qquery 2.1.24 listing for set of presidents after Nixon and before Obama (formerly between LBJ and Clinton)
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: {Ford, Carter, Reagan, G. Bush, Clinton, G. W. Bush} Again, it asks for a “listing” so I used the “Listing Method.” Nixon and Obama are not included in this list, because it clearly says “after” Nixon and “before” Obama. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The solution given here is for presidents between Johnson and Clinton. A listing would be {}{}{ Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Regan, George HW Bush}.{}{}Set-builder notation is {x|x is a president who served between Lyndon Johnson and William Clinton} x is a variable and the condition 'x is a president who served between Lyndon Johnson and William Clinton' tells you what possible things the variable can be. COMMON ERROR: It's incorrect to say {x | x is the set of presidents who served between Johnson and Clinton}. x is a president, not a set of presidents. Should be {x|x is a president who served between Lyndon Johnson and William Clinton} ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I think my answer is correct. You need to up-date the president names in your given answer. ------------------------------------------------ Self-critique Rating: 3
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Infinite: {x|x is a rational number 0 to 1} Rational numbers can be written as a fraction. 0 and 1 are rational numbers and there are many fractions (rational numbers) that can be written between these numbers (more than I can count). confidence rating #$&*: 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): After reading the given solution, I’m not sure if you are saying that it is finite or infinite. ------------------------------------------------ Self-critique Rating: 1
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: n(A)=1 This is referring to the cardinal number of the set which is the number of elements in the set. The set includes a U.S. senator which implies a single person. confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** n(A) stands for the number of elements in the set--in this case for the number of senators. There are 100, 2 from each State. So n(A) = 100. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I messed that one up. Now I see that it was saying that each element was a US senator in a set of US senators (plural). ------------------------------------------------ Self-critique Rating:2 ********************************************* Question: `qquery Is {x|x is negative number} well-defined?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: No, it is not well-defined. All this tells us is that each element is a negative number. It doesn’t define the numbers as whole numbers, counting numbers, rational numbers, etc. It just sounds like it is referring to every negative number in the world which would be very infinite. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): Messed up again. I guess I misunderstood the definition of “well-defined.” I was just thinking that only saying negative numbers was a broad description. I can see I need to use some deeper thinking. ------------------------------------------------ Self-critique Rating: 1