The Venn of my Existence: Week 1 & Week 2

Understanding the complexities of discrete math and mastering the “new language” of logic and mathematical notation is not for the faint of heart. However, the approach going in must be that of learning any new language. At first, the flow is unnatural, the construction of sentences are slow, and the statement which you thought was formulated perfectly is clearly not conveying anything significant (the confused expression of your peers signifies this is the case).  With perseverance and a lot of hard work, perhaps one day I, along with my fellow classmates, can be fluent in logic. Until that point in time, I request that Rosetta Stone get to work on a Logic Language Learning program. I think we all may need it.

Now on to the real part of the blog. Before I am even attempting sentences, I have gone through the interesting experience of trying to verify and falsify statements using Venn Diagrams. Although at first it seems simple, the complexity comes when trying to isolate the minimum values needed to verify or falsity a particular statement. To make the statement “every x in A is also in B” be true, all elements that are in A must also be contained in B, and to falsify it just takes one counter-example. However, the minimal requirement to demonstrate this in a Venn Diagram is to show that the part of A that exists outside the intersection of A & B is empty. I find it confusing that is not a necessity to have the intersection also be occupied in this case. Furthermore, I also realize this changes once real observations are given. Once a list has been given, there is an obligation to show that the intersection is occupied with those observations.  Overall, understanding the minimal requirements for proving a statement true or false statements has been a trying exercise.

For me, the challenge this week has been learning how to eliminate superfluous information and focus solely on the relevant information needed for a particular problem. While this may in theory seem simple, for me, it is definitely proving to be a challenge.