I'm trying to learn something about mathematical logic. I think, I partly understand definitions of free variables, bound variables and quantification, but it's not easy topic for me and it's not enough to solve problems. I mean, for example I have such problem:
mark sets on a graph:
- $\{ z : \mathbb{R} | \forall{x}\exists{x}(x=1) \}$
- $\{ z : \mathbb{R} | \exists{x}\forall{x}(x=1) \}$
- $\{ x : \mathbb{R} | \exists{x}\forall{x}(x=1) \}$
What is $z$ in this case? How to think about such problems? How to solve them?
I'm not asking You to solve that particular problem; I want You to explain me (or give some links to articles, tutorials, books etc.) this topic (free variables,bound variables and quantification).
I would really appreciate You help.