Week 5 - February 9, 2013

Last week I did not post anything as I simply had nothing to say.  We began our introduction to proofs but for the most part I had nothing to write that was worth noting.  However this week I do have a few things to discuss.  We had our first term test yesterday in class.  We were given about 50 mins to complete the test which consisted of 3 questions on 6 pages.  Throughout the week I was a little nervous about the test because I really wanted to do well, not only for academic credit but also for reinforcement.  As I stated in the previous post I am feeling very confident in my understanding of the course material so far.  If there was a concept that I didn't fully grasp I either figured it out through practice problems provided on the course website or through watching lecture videos online.  Having said that, I really didn't want to take this test and find out that in fact I really didn't understand everything that I thought I did.  If however I do well on the test then I will feel that indeed the methods I have been using so far have been working and that my future in the course should be promising.

Now regarding the test, all I can say is that I found it to be very straight forward.  The first problem was about the Python 'quant' functions we had seen before.  This problem tested our understanding of universal and existential quantification, as well as our ability to negate such statements.  The second question involved two statements similar in form to an epsilon-delta proof.  It asked to negate each statement and determine which of the two, the original or the negation, was true and to explain why.  The last question involved an English statement.  We were asked to write in symbolic form the contrapositive, converse and negation of the statement.

I look forward to receiving the results of the test as I feel I did very well.  I completed the test in about 30 mins and had ample time to review the test once over.  The only thing that still bothers me in terms of course material is when we are asked to write the negation of an implication.  Now I feel very comfortable with negation, however at the beginning of this course we learned that the contrapositive of say S1: A -> B is

Not B -> Not A.  The converse would be B -> A, and what was called the negation would be 

Not A -> Not B, however on Wikipedia at least, this is not referred to as negation but rather the inverse of S1.  So negating both sides of an implication is really called the inverse and not the negation of the implication.  Instead, the negation of S1 would be A ^ Not B, (read as A and not B).  Now A and not B is not the same as: If not A then not B, which is the inverse, so clearly the inverse is not the same as the negation of an implication.  So on the test for example, when we were asked for the negation, I simply wrote A ^ Not B, A being the antecedent and B being the consequent.  I do hope that this is correct and that I wasn't really asked to provide the inverse of the implication.  So at this point I see the inverse and the negation as being two separate things.  I'm still not sure if this is correct or not; in any case I wonder why we referred to the inverse of an implication as the negation at the beginning of this course?