Hello I am attempting to teach myself abstract algebra using FM Hall's "Abstract Algebra". The first section is an introduction to set theory which I get concepotually but when goigng through the excercises at the end of the chapter I got completely thrown by the following,

Proove:

A is contained completely in B <=> for all elements x which are not elements of A are elemets of B

How do I go about prooving this. Thanks for any help with this.

(This place could do with a maths notation font or summit )