# Free variables, bound variables and quantification - explanation

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.

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The three bulleted expressions don't make any sense to me. – Christian Blatter Jan 23 '11 at 9:44