What can be in variable? (First-order logic) We learn First-order logic, and we learn about terms at Formula rule (https://en.wikipedia.org/wiki/First-order_logic#Formation_rules) 
My questions is:
We learn that each language have terms: constants, functions, variables,...
Variable $x$ can be only a constant? or it can other things? like if we have constant $C$ and function $f(t_1)$ ($t_1$ is a term), so $x$ can be equals to $f(C)$? or $x$ can be only equals to $C$?
I don't understand it well...
Thank you!
 A: Variables and constants are symbols.
The set $\text {Var}$ of variables of the language and the set $\text {Cons}$ of constants of the language must be disjoint :

$\text {Var} \cap \text {Cons} = \emptyset$.

Constants are "names" used to denote objects of the domain of interpretation, like e.g. $0$ for the number zero.
Variables are used to write quantified formulas, like e.g. $\forall x (x \ge 0)$.
"Complex" terms are built-up with variables, constants and function symbols (from a new set $Fun$ of symbols): $+$ is a binary function symbol and with it we can write e.g. the term : $x+0$.
When we interpret a formula, we have to assume a domain (a collection of "objects") like e.g. the set $\mathbb N$ of natural numbers and suitable interpretations for constants and function symbols.
The variable must be interpreted according the formal specifications of the semantics of the language: in a nutshell, the formula $\forall x (x \ge 0)$ is true in $\mathbb N$ because all natural numbers are non-negative.
A variable in an open formula, like e.g. $x=0$ acts as a pronoun (compare with: "it is red"): the formula per se has no meaning. 
In order to give meaning to the formula we have to assign a "temporary" denotation to $x$: the way to do this is defined by the semantical specifications.
We may choose different examples, with the "universe" of humankind as domain of the interpretation.
Consider now the open formula:

"$x$ is father of Abel". 

If we assign to the varibale $x$ Adam as denotation, the resulting sentence is true; if instead we assign Cain to $x$, the resulting sentence is false. 
If we quantify the formula, we have : "$∀x (x$ is father of Abel)", that is false, and "$∃x (x$ is father of Abel)", that is true.
