logical functions graph (there exists x in R so x^2+y^2=1, etc)

[mathnotmypassion]

Assuming that x and y run through the set R, find the graphs of propositional functions:
$$∃_{x∈R} \quad x^2 + y^2 = 1, \newline ∃_{x∈R}\quad x · y = 1, \newline ∃_{x∈R}\quad x · y = 0, \newline ∀_{x∈R}\quad x^2 + y^2 = 1, \newline ∀_{x∈R}\quad x · y = 1, \newline ∀_{x∈R}\quad x · y = 0$$HELP, tell me how to solve this. I know that first equation gives circle in coordinate system and chart $$\{y\in \mathbb{R}: ∃_{x\in \mathbb{R}}\; x^2+y^2=1 \}=<-1,1>$$with note: the set y for which the horizontal line intersects the graph at least once
I dont know why things are like that
English is not my language, if possible, I would like to ask for a link to videos/courses on youtube that could explain it to me. I don't know how to search for logic topics in English