How is the math term "such that" represented in pure AND/OR logic? I know how the notation for "such that" looks like when talking about sets, but I don't understand how it's represented logically in terms of AND/OR and conditional IF statements.
To clarify my question, how would one represent the logic of "such that" in computer software? After all, the meaning of "such that" is a constraint, so does it mean that I would simply translate "x such that y>0" to "x AND y>0" ?
Or maybe it should be "If y>0 then x"?
Thanks
 A: In discussions of sets, the phrase "such that" is usually encountered between bound variables and predicates in either predicate logic statements or in set builder notation (where the predicate is a constraint).   Often both at once.
$$\{x\in \Bbb Z \mid \exists n\in Z:(2n=x)\}$$
This may be pronounced: "The set of integers $x$ such that there is some integer n such that $2n=x$."

In predicate logic statements, the colon is an optional punctuation mark to make the statement parse better.   It may be omitted without impacting the statement, but helps visually separate the predicate from the bound variable.   $\forall x\in \Bbb R: x^2\geq 0$ has the same meaning as $\forall x\in\Bbb R~~x^2\geq 0$, however some clarity may be lost.   Parenthesis serve the same purpose.
However, in set construction notation the separator is mandatory; though a vertical bar or a colon may be used, depending on available typesetting or style choice.
A: Usually when we use set-builder notation, we have something like,
$$S = \{ \text{some expression involving x} | \text{ some condition on x}\}.$$
Suppose we put all the elements that satisfy the condition and put them in a set called $A$ and let's denote the expression involving $x$ as $f(x)$. Then we can write,
$$S = \{ f(x) | x \in A\}$$
and say
$$x \in A \implies f(x) \in S.$$
