(a) (Russell paradox) A logical difficulty arises from the idea, which atfirst appears

Chapter 2, Problem 3

(choose chapter or problem)

(a) (Russell paradox) A logical difficulty arises from the idea, which atfirst appears natural, of calling any collection of objects a set. Lets saythat set B is ordinary if For example, if B is the set of all chairs,then because B is not a chair. It is only in the case of very unusualcollections that we are tempted to say that a set is a member of itself.(The collection of all abstract ideas certainly is an abstract idea.) LetX = {x: x is an ordinary set}. Is Is What should we sayabout the collection of all ordinary sets?(b) In the town of Seville, the (male) barber shaves all the men, and only themen, who do not shave themselves. Let A be the set of all men in thetown who do not shave themselves. Who shaves the barber? (That is, isthe barber an element of A? Is he not an element of A?)