Proofs

I completely forgot to keep updating my blog here. Regardless, I'll share a quick recap of the past few weeks and my thoughts about the course so far.  For the past weeks, we've covered a lot of topics - negation, implication, proof structure, and introduction to proving.  The class didn't start off as hard as I thought given how unfamiliar I am with mathematical symbols.  Working through negation problems seems like just working through problems with a set of equations (being able to covert all the statements into its negated version).  There really isn't much thinking involved.  As long as you understand what all the parts of the statement is saying, it is quite straight forward.

What interested me a little was the difference between implication and conjunction.  In my first glance, I thought for all x , P(x) --> Q(x)  is the same as for all x,  P(x) and Q(x).  In my opinion, the easiest way to tackle the difference between these two statements is by drawing their respective Venn diagram.  When drawing their Venn Diagram, we notice that there are are a lot more flexibility in terms of what kind of values we can have in the implication.  For the implication, as long as P(x) is empty, the statement is true.  However, for the conjunction to be true, all values must be in the intersection of P(x) and Q(x). This was the subtle difference I noticed while working through the problem through a Venn Diagram perspective.

Lastly, just this past week, we started looking into proofs.  For the first week, it was a relatively straight forward topic.  We looked at the valid proof structures this course required of us.  But the actual proofs is the part where I am starting to have some trouble.  It is relatively hard for me to find the "light bulb" for the different proofs.  In that sense, I hope to improve in my ability to find the connecting link for various proofs.

Cheers