  We address the problem of deriving the set of quantum correlations for every
Bell and Kochen-Specker (KS) contextuality scenario from simple assumptions. We
show that the correlations that are possible according to quantum theory are
equal to those possible under the assumptions that there is a nonempty set of
correlations for every KS scenario and a statistically independent realization
of any two KS experiments. The proof uses tools of the graph-theoretic approach
to correlations and deals with Bell nonlocality and KS contextuality in a
unified way.
