Any ideas?

Show that the set of all x such that x is in A and x is not in B exists.

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- Sep 7th 2009, 06:53 AMqwe123Axiom Question
Any ideas?

Show that the set of all x such that x is in A and x is not in B exists. - Sep 7th 2009, 07:23 AMTKHunny
Two things come immediately to mind:

1) Is B not A?

2) Define "exists". "Contains at least one element"? - Sep 7th 2009, 07:57 AMThePerfectHacker
- Sep 7th 2009, 08:46 AMTaluivren
Hi,

what are $\displaystyle A,B$? sets?

if they are sets, then the axiom schema of restricted comprehension, namely the axiom $\displaystyle \forall b\forall a \exists z \forall x (x\in z \leftrightarrow (x \in a\,\&\, \phi(x,b)))$ where $\displaystyle \phi(x,b)$ is the formula $\displaystyle x \not \in b$, ensures existence of the set you described (just evaluate $\displaystyle a$ to be $\displaystyle A$ and $\displaystyle b$ to be $\displaystyle B$)