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I'm taking a discrete mathematics course. We are covering logic and proofs in the current section, specifically argument form and validity. I am doing one of the practice problems which is similar to an assigned problem that I must turn in for credit, and the provide answer to the practice problem seems to contradict what is said in the text, as well as contradict itself. There is either a mistake, or I am somehow mistaken.

So here is the basis of what I'm doing. The problem is to construct a truth table from a set of provided premises and a provided conclusion. The truth table will indicate whether or not the the argument has valid form. This is done determining if the truth value of the conclusion is true wherever all premises are true. I am also instructed to highlight the premises in the truth table.

So when setting up the truth table I break the premises down to there individual components and expand out to the whole of the premises. The most basic of individual components are p, q, and r. But then there are inverses and possible combinations of these that may be part of the problem, but as I understand, are not part of the premises as a whole. In the appendix all components other than the most basic p, q, and r, are being marked as the premises. Earlier in the chapter it is not explained this way. One is not to even test the conclusion for it's truth value unless all premise of the same row are true, and some of the components in which the example has marked as being part of the premises aren't even true, and the book still tests the conclusion for it's truth value there. What is actually part of what I believed to be the premise is in fact true in these rows though, making it rightly so that the conclusion should be tested for it's true or false value.

I hope what I am explaining is understandable, as I'm new to this branch of mathematics so I'm a little fuzzy on my explaining abilities here. I will upload some pictures of what's happening.

From the chapter:
Example From Chapter

The above example shows that the only part being marked as the premises are the actual parts that are wholly in the originating argument. This is from the textbooks chapter on this subject .

From the appendix:
Argument and Solution from Appendix

The above example is from the Appendix which provides an example answer to one the questions at the end of the chapter. As you can see it has marked the individual component of NOT q as one of the premises. NOT q does not show up on its own in the individual argument, and it isn't even true in the last 2 rows in which the conclusion was tested. What I perceive to be the premises are the three columns to the right of NOT q. I don't think NOT q is supposed to be part of the premises. I just want to get it right so I can turn in accurate work. Either the answer to the example question provided is wrong, because it seems to differ from what the example in the chapter shows, or I am missing something. Please advise.

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It's a typo in the part you quote from the appendix.

The column headed $\sim p$ should not have been part of the "premises" bracket.

(Note that this column does not even have a T in the line that the blue comment states to "have true premises").

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    That was my interpretation also. The messed up thing is that all of the examples for problems of this type in the appendix are done this way (incorrectly). I guess I will turn in my versions with the true premises under the bracket. I just hope the professor for the class doesn't have the same incorrect type answers from the book for his grading key. If that is the case then I'll likely loose points for turning in correct work. – 2017-02-04
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    @PhilFernandez: Don't fret -- unless you're studying somewhere extremely subpar, people wouldn't be tasked with teaching or grading such a course unless they _know how these things work_ themselves and will be able to spot such obvious typos in an answer key just as well as you and I. – 2017-02-04