Assignment 12 text

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20:41:33 Query 3.1.10 Mary is top grossing film. Is this a statement?

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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems. yes, it can be proven as true or false.

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20:43:01 ** 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 --> I took top-grossing as a monetary statement which can be proven, but I see what you are saying.

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20:43:20 Query 3.1.12 sit up and behave Is this a statement?

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RESPONSE --> No, it is a command.

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20:43:28 ** 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 --> ok

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20:44:48 Query 3.1.18 Is this a compound statement or not: 'calif or bust'.

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RESPONSE --> #20 is not a compound statement. The ""or"" is part of the title of the sign.

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20:46:32 ** 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 --> But how do we know that is what it means? Just as in the previous problem, it isn't stated explicitly. I thought if ""or"" is in the title of something in a sentence, it isn't considered the context for a compound statement.

You wouldn't necessarily know the context; in the absence of the context, your explanation is perfectly valid and would be given full credit.

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20:46:48 Query 3.1.30 negate 'some people have all the luck

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RESPONSE --> NOt all the people have all the luck.

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20:48:48 ** 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 --> I see that not all people and some people are equivilant.

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20:49:33 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 years old.

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20:49:39 ** The statement is 'She has green eyes or he is 48 yrs. old' **

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RESPONSE --> ok

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20:50:03 Query 3.1.48 What is the statement -(p disjunction q)

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RESPONSE --> She does not have green eyes or he is 48 years old.

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20:52:32 ** 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 --> So, the sign would be flipped in this negation? ""Or"" becomes ""and""? I didn't notice that anywhere in the text.

This is one of deMorgan's laws. I believe those laws are still in section 1, though I don't have the text and they could have slipped a change past me in the latest edition.

In any case be sure you note and understand deMorgan's laws when you do encounter them; they are definitely there, and fairly early in the chapter.

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20:53:09 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 --> ~ (q V p)

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20:55:14 ** 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 --> Why does (p V q) have to be included in the final answer?

You are correct. (p U q) ^ ~(p ^ q) is equivalent to just ~(p ^ q).

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20:56:20 3.1.60 true or false: there exists an integer that is not a rational number.

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RESPONSE --> false

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20:56:34 ** 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 --> ok

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20:56:58 Query 3.1.66 true or false: each rat number is a positive number

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RESPONSE --> false

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20:57:06 ** 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 --> ok

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20:59:44 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"" means all students failed. Nobody passed. ""Not all students passed the test"" means some or at least one student(s) passed.

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21:00:09 ** 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 --> ok

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Very good. See my notes and let me know if you have further questions.