Third week: Proofs

This tutorial we did proofs. At first I was confused about proofs because I didn't know whether to negate them or use the rules; I only understood how to negate statements, not prove them.
So I didn't really understand the first tutorial question, but I got the second one. I was also confused about the third one because I thought it involved vacuous truth and I got the opposite answer than the answers the TA gave.

Then today I went to office hours and it cleared it up for me. 
I still find the logical notation very confusing; just when I think I have understood it and grasped the concepts, I forget it and have to relearn it and look at it over and over. Hopefully I'll soon be familiar enough with it for it not to be confusing anymore.

I put:

(A ^ B) => C
But the answer was:
(A V B) => C
And then I subbed in the statement:
If the temperature is hot, or the sun is shining, then it's swimming weather.
When looking at this statement, I didn't know if both A and B were needed for the statement to be true or not. That's why I was confused. I didn't know which one was right.
After office hours today, I saw how (A V B) => C could change to (A => C) ^ (B => C) by using the identities, distribution, and DeMorgan's law.

(A V B) => C
¬(A V B) V C
(¬A ^ ¬B) V C
(¬A V C) ^ (¬B V C)
(A => C) ^ (B => C)

As for the proofs, I now realize that I have to negate them, and I DO have to use DeMorgan's law and the other laws.

I still have trouble with them, but hopefully I can get them down by the test next week.