assignment #012 012. `query 12 College Algebra 03-01-2009
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15:14:50 Query 3.1.10 Mary is top grossing film. Is this a statement?
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RESPONSE --> No it is not a statement because it is not well defined. confidence assessment: 1
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15:15:03 ** A sentence is a statement if it is true or false. Otherwise it is not a statement. 'There goes a big one' is not a statement because the word 'big' is open to interpretation so is not a statement. 'There are 3.87 * 10^89 particles in the universe at this instant' is a statement: it is either true or it isn't, though we don't know enough to tell which. The gross receipts for a film can be regarded as hard facts--unlike opinions on whether a film is good, or artistic. If 'a top grossing film' is defined as, say, a top-10 film in gross receipts, then we could ascertain whether it is true or false and we would have a the statement. However, 'top grossing' isn't defined here--does it mean one of the top three for the week, top 10 for the year, or what?--and for that reason we can't decide for sure whether it is true or false. So this sentence couldn't be regarded as a statement. **
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RESPONSE --> correct self critique assessment: 3
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15:16:01 Query 3.1.12 sit up and behave Is this a statement?
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RESPONSE --> No, this would be considered a command. confidence assessment: 1
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15:16:10 ** This is not a statement. It is a command. You could evaluate the truth of the statement 'you sat up', but not the truth of the command to sit up. **
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RESPONSE --> correct self critique assessment: 3
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15:18:34 Query 3.1.18 Is this a compound statement or not: 'calif or bust'.
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RESPONSE --> Yes, because it is 2 statments combined with ""or"". confidence assessment: 2
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15:18:45 ** The meaning of the phrase is actually 'we're gonna get to California or we're gonna break down trying', in which context it is a compound statement involving 'or'. **
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RESPONSE --> correct self critique assessment: 3
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15:20:02 Query 3.1.30 negate 'some people have all the luck
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RESPONSE --> The negate would be 'all people do not have all the luck'. confidence assessment: 1
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15:21:35 ** The negation would be 'all people don't have all the luck', which means 'nobody has all the luck'. The negation of 'some do' is indeed 'all do not', which is the same as 'none do'. The negation of 'all do' is 'some do not'. The negation of 'none do' is 'some do'. COMMON ERROR: Not everyone has all the luck, or equivalently some people do not have all the luck. This is not incompatible with the original statement, and the negation must be incompatible. Both would be true if some do have all the luck and some don't. **
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RESPONSE --> correct self critique assessment: 3
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15:24:13 Query 3.1.42 p: she has green eyes q: he is 48. What is the statement (p disjunction q)?
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RESPONSE --> She has green eyes or he is 48. confidence assessment: 1
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15:24:22 ** The statement is 'She has green eyes or he is 48 yrs. old' **
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RESPONSE --> correct self critique assessment: 3
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15:25:31 Query 3.1.48 What is the statement -(p disjunction q)
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RESPONSE --> It is not the case that she has green eyes or he is 48 years old. confidence assessment: 2
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15:25:40 ** The correct translation is 'It is not the case that she has green eyes or he is 48 yrs. old'. An equivalent statement, using deMorgan's Laws, would be 'she doesn't have green eyes and he is 48 years old' COMMON ERROR: She doesn't have green eyes or he is not 48 years old. This statement negates p V q as ~p V ~q, which is not correct. The negation of p V q is ~p ^ ~q. **
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RESPONSE --> correct self critique assessment: 3
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15:30:00 Query 3.1.54 Jack plays tuba or Chris collects videos, and it is not the case that both are so
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RESPONSE --> ~(p v q) confidence assessment: 1
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15:33:10 ** The statement 'jack plays or Chris collects' is symbolized by (p U q). The statement that it is not the case that both are so is symbolized ~(p ^ q). The entire statement is therefore (p U q) ^ ~(p ^ q).**
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RESPONSE --> I missed this one. I don't really understand where the U comes from. Can you explain this one for me please? self critique assessment: 2
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15:34:41 3.1.60 true or false: there exists an integer that is not a rational number.
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RESPONSE --> False because any interger can be a rational number. confidence assessment: 1
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15:35:02 ** A rational number is a number that can be written as p / q, with p and q both integers. Examples are 2/3, -5489/732, 6/2, etc.. Other examples could be 5/1, 12/1, -26/1; these of course reduce to just 5, 12, and -26. The point is that any integer can be written in this form, with 1 in the denominator, so any integer is in fact also a rational number. Thus there is no integer that is not a rational number, and the statement is false. **
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RESPONSE --> correct self critique assessment: 3
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15:36:58 Query 3.1.66 true or false: each rat number is a positive number
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RESPONSE --> False because a rational number can be a negative. confidence assessment: 1
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15:37:06 ** This is false, and to prove it you need only give an example of a rational number that is negative. For example, -39/12 is a rational number (integer / integer) and is negative. **
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RESPONSE --> correct self critique assessment: 3
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15:41:13 Query 3.1.75 difference between 'all students did not pass the test' is the statement ' not all students passed the test'
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RESPONSE --> All students did not pass the test includes all the students and not all students passed the test includes that some did actually pass the test. confidence assessment: 1
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15:41:34 ** The first statement says that 'all students did not pass', meaning every student didn't pass, i.e., nobody passed the test. The second statement says that not everyone passed--at least one student didn't pass. The second statement doesn't address the question of whether anyone passed or not, so it doesn't necessarily say that some students did pass, but it leaves open the possibility that some did. Since the second statement contains possibilities the first does not the statements are not equivalent. **
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RESPONSE --> correct self critique assessment: 3
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