Barber Paradox/Resolution 3

Resolution
Let the every condition above be relaxed, and rewrite it as:
 * his task was that he may shave only men in the community who did not shave themselves.

The initial premises can be coded:
 * $(1): \quad \forall x \in \mathbb U: \map B x \implies \paren {\neg \map S x}$
 * $(2): \quad \map B b \iff \map S b$

Thus it is not the case that:
 * $\paren {\neg \map S x} \implies \map B x$

However, from $\map B b \iff \map S b$ this then means that $\neg \map B b$.

So at least one person in the community is not shaven by $b$ at all, the barber himself necessarily being one such.

This of course does not preclude the possibility that some other person, who is not the barber, may also shave people.

These may or may not include the barber, who may retain his beard.