a little bit suffering

This weeks classes are about quantifiers, sentences, symbols and implications. All of those things come into my mind in a week which makes me feel a little bit confused. I think I need to organize them in this weekend. Quantifiers and sentences do not mess me up, but implication does.

Symbols are the easiest one for me, thanks for MAT223!!!  In this semester Mat224 also include symbols. But there is a new one the symbol of negation, if I understand correct this symbol means non or not.

I want to say something about implication. In English, the definition of implication is "if...then".  In other words, implication means giving a qualification and then geting a result. The following sentence is an example: " if today is raining, then you will need to bring an umbrella.  But I am not very clear about the contrapositive and converse.The original implication is "if x, then y". In my opinion, the contrapositive for that is " if non-y, then non-x".  Also I think in contrapositive, if the original implication is True, then the contrapositive of that implication is True.The definition of converse in logic is the same as its English meaning . Also in my opinion, the original implication is 'if x, then y' and this is True. The converse of that implication is 'if y, then x' but we cannot figure out whether this is True or False. For example, in calculus, my high school teacher said if a function is differentiable on it domain, then it is continuous on its domain, but if a function is continuous on its domain, we don't know that is differentiable on its domain and the counter example is y = abs (x). I hope my understanding is right. 

Finally, I want to thanks for the tutorial problem set, because that helps me understanding the Venn diagram. It's really helpful.