Weeks 2 & 3 - Implication, Conjunction, Disjunction, Negation. Good Thing There's Truth Tables!

Just another way of saying “if/then”, “and”, “or”, “not”. I have to say, implication was the most challenging. It's the odd one out of the group and I always have to think of it in terms of the other three. We all grew up saying “ands”, “nots” and “ors” but who grows up making implications all the time? This helps me translate it into something I am familiar with. Some of you might not agree, but “don't knock it unless you've tried it”. Or is it “don't knock it if you haven't tried it”? I was really surprised to see this broken down to “if you've knocked it” it implies “you've tried it”. Seems like an odd way of thinking. I had to decipher this problem using Venn diagrams, sets, and complements before I was convinced. And then I realized that the two “nots” in the original sentence created a contra-positive to the final translation. I'll have to remember to look at the lecture notes the next time I get stuck on a problem like that. I'm sure they'll help with completing the assignment.

Negating expressions is not bad. The concept seems fairly straightforward. Negation ties in very well with verifying and falsifying universal and existential quantification. Conjunction and disjunction was like a repeat of the first two weeks of statistics which I am also taking this semester. Actually, most of the stuff about sets was contained in there as well. Of course we are taking a much more abstract approach. Have you noticed that on Assignment 1 we only had one problem with numbers and the rest was translating stuff to and from English? For the most part these three alone are not a problem but when you combine them with implication and make longer expressions it gets very confusing, even with Venn diagrams.

Thank goodness we have the mighty truth table! I can draw straight lines no problem, I have a ruler! But circles freehand are not a walk in the park. Truth tables are great for breaking down those larger problems into the smallest operation to the point where all you have to do is think yes or no, true or false, on or off. Yes I know, like a computer. With Venn diagrams you almost had to solve the entire expression for every single region just to know whether it was occupied or not. I look forward to doing more work with truth tables and I'll have to keep Venn diagrams in my back pocket (I doubt they're going to ask us whether Al makes more than $60,000 on a test).