Thread: Axiom Question

Any ideas?

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

Two things come immediately to mind:

1) Is B not A?
2) Define "exists". "Contains at least one element"?

Originally Posted by qwe123

Any ideas?

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

Define the property statement P(x) to mean "x is not in B".
By the Axiom Schema of Comprehension there is a set S such that x is S if and only if x in A and P(x) is true, that is, x is in A and x is not in B.

Hi,
what are ? sets?
if they are sets, then the axiom schema of restricted comprehension, namely the axiom where is the formula , ensures existence of the set you described (just evaluate to be and to be )