Week 5

Test #1 was not too bad. The only part I didn't understand was the question where the 2 logic statements were identical, except for the order of quantifiers. I didn't know this mattered. I always assumed ∀x, ∃y was the same as ∃y, ∀x. However, I checked over the Wikipedia page on Quantifiers and it seems of course it does matter.

They used the example ∀x ∈ N, ∃y ∈ N, y = x^2 and ∃y ∈ N, ∀x ∈ N, y = x^2. The first statement is true, but the second is false. Previously, if they were written symbolically, I would have said both are true. When I write them in English, it's of course a lot easier to understand and explain why both are not true. Actually, even if you wrote them as Python/pseudo syntax with proper nesting, it would be better.

all(any(y==x**2 for y in naturalNums) for x in naturalNums)

any(all(y==x**2 for x in naturalNums) for y in naturalNums)

Week 4

I found the assignment to be reasonably easy for the most part. 2d) really tricked me. I saw it was the inverse, but decided to word it as "the converse of the contrapositive" which I thought would be a safe bet. Initially I found number 4 hard, which probably should have been the easiest one, but quickly figured things out once I realized that some of the sections could be empty. It was late and I shouldn't have assumed that. Lastly on number 5, Professor Heap explained in class it could be both, so I assumed there must be one that was both. I couldn't find one that was, but in the answers it appears that, of course, there was. Now it's time to make the aid paper for the test on Wednesday and luckily the notes include a couple handy and comprehensive pages of logic formulas.