ALL you need to know about assignment 2

Hey again

I know it is sort of late to talk about assignment 2. However, I just noticed that while other blogs have intensively discussed assignment 2, I have only briefly mentioned it in the previous post and thus figured out that I should give the assignment more credit so here you go,

EVERYTHING YOU MAY (or may not) WANT TO KNOW ABOUT ASSIGNMENT 2:

• BEFORE:

In general, I think most students in this course (including me) prefers proofs to the first part of the course; they are challenging, fun, and you feel pretty smart once you have finished one.

However, most of us (again, including me) were worried that we won't be able to solve proofs we have never seen before.

• DURING:

Luckily, I think the assignment was quite fair in terms of easiness especially that tons of office hours were available.

However, it is important to note that this assignment was our first major course work regarding proofs. And as you might expect, different people had different opinions about the assignment. 

Here are some I quote from other blogs/slogs:

http://165uoft.blogspot.ca/ :I found this assignment wasn't as bad as the first. I'm finding this one more concise in terms of its statements. The hardest question I would have to say is number 6 as it utilizes a small trick

http://annakovale.blogspot.ca/: I think Assignment 2 was great practice for proofs and I liked it more than the first assignment (I like proofs)...... I feel like it deserves a separate post.

http://slogjourney.blogspot.ca/:Oppose to watching the professor write the proofs and unanimously agreeing, this assignment was great practice in independently building up my proofs.

So, overall, the assignment was a great chance to practice for the test.

and as you might expect lots of questions were asked:

Here are couple of questions posted by http://1d10terror.blogspot.ca/:

is if there is a statement that I know a counter example for, can I state the counterexample and reach the conclusion thatP(x) -> notQ(x) for all values? Will that be enough to invalidate the entire statement? Also if I have a statement that has a for all assertion in the consequent, what on earth do I do? For example x in D, P(x) -> ( y in D, Q(y) ^ P(y)), is there anything I can do to solve this or am I completely boned and should view the statement from a different angle?

again, I know I am answering these after the assignment but I guess, it is better than never (we still have an exam to write anyway).
So here is my attempt at answering these questions:

1.     If you are trying to negate P(x) -> q(x), you shouldn't prove that p(x)-> not q(x) since this (as discussed in class) is proving "too much" than what you actually need to prove all you need is one example in which P(x) is true and q(x) is not 

2.     proving a for all in the consequent should be treated as any for all: by assuming that y is a generic element of D and then trying to prove that the predicates p and q apply to every single element in D (by proving that they evaluate as True to the generic element y). It might have been confusing due to the many /for alls/ . Personally, what I do to minimize confusion is to go over the statement from left to right in order, writing assume...... for every for all or implication, pick... for each there exists. This way by just building the "skeleton" of the proof, you have given yourself a head start to how your proof will look like and what exactly do you need to find out (to fill in the blanks).    

• AFTER:

I think the assignment was a really good exercise and an awesome preparation for midterm 2. Proof: most people did well on term test 2.