1. Russell’s paradox is equivalently formulated as the Barber Paradox: In a town there is a barber who shaves all the men that do not shave themselves, and only those men. Define ‘‘set’’ A as the set of all men in the town that the barber shaves.

(a) Is the barber a member of this set? Show that the barber’s set membership cannot be determined as we would conclude the paradox that the barber shaves himself if and only if he does not shave himself.

(b) Note that the paradox works because at the time, the barber was assumed to be male. Show that if the barber were female, we could conclude that the barber is not a member of this set, whether she shaves or not.