Struggling with Relation in maths

[Nemanja]

Basically I have exam in few upcoming days, and I wasn't attending first couple classes regarding relations so therefore I have no clue what is going on.
Ive been searching a lot on google and can't seem to find anything to start out with. Signs are the hardest problem, if I may knew that I could start with something.
Lets just say I dont know anything and just wanna start from scratch. I just want someone kind enough to name me all the signs, for example: A(turned upside down) what does it mean, just someone please tell me what the signs mean or symbols whoever u wanna call it. I will put my test how it looks ( words are on my language so just see the symbols) and you can see the symbols there and have a bigger picture of what Im talking about. Thanks in advance you kind people.

 

[Zermelo]

Hi there, I can’t really help with explaining the whole subject, but I can recommend some resources. I see that you’re probably from Serbia (ja sam iz Bosne ?), and a really good Set Theory worksheet is by Renata Turkeš: https://132467e1-5067-00f7-b135-ff7...d/eb99bb_559d75cc8655435a877855e400c0f2f5.pdf
If you want to learn the theory behind it, I can send you the literature by Nermin Okičić in inbox.
"A" upside down means “for all”, so the sentence [imath]\forall x \in R, x^2 \geq 0[/imath] means that "For every real number x, it's square x*x is non-negative", aka the square of every real number is non-negative.
Let p be a relation (for example >=, =, or ||) on set A. We say that 2 elements of set A, let's call them x, y are in a relation p iff (x, y) is in p (p is a set of ordered pairs) [imath]x\ p\ y \Longleftrightarrow (x, y) \in p[/imath]. So, instead of saying [imath]3^2 = 9[/imath] we can say [imath](3^2, 9) \in "="[/imath], if that makes any sense, this is a formal way of dealing with relations. Also, [imath](2, 4) \in "\leq"[/imath].