course Mth 151
solution to stated problem does not match the given solution, you should self-critique per instructions at
http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm
Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
012. `query 12
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `qQuery 3.1.10 Shrek is top grossing film.
Is this a statement?
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Your solution: yes because it can either be true or false.
Confidence Assessment:
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Given Solution:
`a** 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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Self-critique (if necessary):
I see why it would not be a statement.
Self-critique Rating:
Question: **** `qQuery Not assigned, but you should be able to answer: Is 'Sit up and behave.' a statementlineCount = lineCount + 1: bLine$(lineCount) = ""
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Your solution:
I don? understand what these mean but I do know that sit up and behave is a compound statement.
Confidence Assessment:
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Given Solution:
`a** 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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Self-critique (if necessary):
I see why it would not be a statement. I was thinking it was combining tow statements.
Self-critique Rating:
Question: **** `qQuery 3.1.30 negate 'some people have all the luck
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Your solution:
All people have no luck
Confidence Assessment:
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Given Solution:
`a** 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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Self-critique (if necessary):
I changed everything is it still right?
'all people don't have all the luck' would have been a little better, but you pretty much did the right things.
Self-critique Rating:
Question: **** `qQuery 3.1.42 p: she has green eyes q: he is 56. What is the statement (p disjunction q)?
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Your solution:
She has green eyes or he is 56 yrs old.
Confidence Assessment:
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Given Solution:
`a** The statement is 'She has green eyes or he is 48 yrs. old' **
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Self-critique (if necessary):
I thought he was 56?
Yes. The book switched ages on me and I didn't get all the edits right.
Self-critique Rating:
Question: **** `qQuery 3.1.48 What is the statement -(p disjunction q)
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Your solution:
It is not P or Q
Confidence Assessment:
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Given Solution:
`a** 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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Self-critique (if necessary):
I didn? realize it was still talking about green eyes and age I thought I had to put the expression in words.
Self-critique Rating:
Question: **** `qQuery 3.1.54 Jack is an English Major or Chris collects DVDs, and it is not the case that both are so
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Your solution:
P V Q
Confidence Assessment:
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Given Solution:
`a** The statement 'jack English 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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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q3.1.68 (formerly 3.1.60). This was not assigned, but you should be able to reason this out: {}{}True or false: there exists an integer that is not a rational number.
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Your solution:
This would be false because 5 and 0 can be integers and rational numbers.
Confidence Assessment:
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Given Solution:
`a** 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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Self-critique (if necessary):
Self-critique Rating:
Question: **** `qQuery 3.1.74 (was 3.1.66) Not assigned, but reason it out: True or false: each rat number is a positive number.
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Your solution:
False not all rational numbers are positive.
Confidence Assessment:
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Given Solution:
`a** 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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Self-critique (if necessary):
I didn? give an example I just knew.
your statement was fine
Self-critique Rating:
Question: **** `qQuery 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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Your solution:
All students did not pass the test is an universal quantifier.
Not all students passed the test is an existential qualifier.
very good
Confidence Assessment:
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Given Solution:
`a** 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. **
The books directions called for which quantifier and that is why I answered this way.
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&#Good work. See my notes and let me know if you have questions. &#