The Sophict and the Problem of Non Being

The problem of non being comes ut because they want to say that falsehood is real. The stranger says, but wait, the sophist wold deny there's any such thing as falsehood. And parmenides, where i come from, has said that there's no such thing as non being. So what's the problem with not being? Anyway? Parmenides might have had a particular problem with non being in there's no real comment on that in the Sophist. But if your concern is falsehood, as plato's concern was in the sophist, you might think that the problem of nonBeing concerns states of affairs that don't obtain. Could you bemet eampe