looking for set theory problems or exercises WITH solutions

Question

I have a problem in that I have a burning desire to master set theory and cannot find worksheets with solutions dealing with elementary set theory.

This is a really big chink in my chain in that if I can master the basic notions of set theory then I am up and away when it comes to mastering the deeper notions, such as the Borel hierarchy.

My assumption is that mathematics is understood by doing, something which I have experienced first-hand and second-hand through others’ statements in this regard. Thus having worksheets with solutions is vital. I already have a grasp over the concepts in set theory, but am hamstrung by not being able to do the mathematics.

Possible solutions to my problem of finding solutions, has been to get various text-books, e.g. joy of sets and kunen’s, trawl various opensource websites and even university looking for the basic worksheets, but I sense a certain caginess. I wonder whether this is due to the effort required by whatever course convener to write up worksheets?

What I do have is the understanding of the philosophy and notions in the subject, and further I can mostly understand set theoretic statement/equations, its just when actually doing the mathematics I am lacking. Thus the main problem is to find set-theoretic mathematical problems to chew over but invariably they do not have solutions to problems given. What they do have are proofs of the complex problems, something which is of utility to me given that I can then seek to prove the proof myself; thus getting insight through doing, but this is out of reach given that I lack knowledge of the basics.

If somebody could send me their coursework, such as homework exercises/tutorial exercises with solutions, or even links to resources I would be forever grateful.

Answer 1

I would highly recommend Velleman's book "How To Prove It" it provides a solid foundation of the basics of logic, set theory, and proofs and has plenty of exercises with solutions.

Answer 2

thanks, but im going to crack on with the advanced topics, which have proofs given after the author has presented the theorem. with this i am going to attempt to prove the theorem on my own and relying on the proof as a check on my attempt.

the utility of this approach is that as the proof/concept being given is undergirded by the basic notions of set theory: concept of a cardinal, union intersection etc. given that i have a pretty firm conceptual grasp of them this will not be completely impossible. however given that i am leaping into the deep end of the set theory, without having practiced butterfly strokes, drowning is likely. what makes it less likely/mitigates it, is that i have thoroughly practiced free-form swimming. what i mean by this metaphor is that i have the meta-knowledge of self-learning/free-form swimming, in that i understand that the deeper concepts/advanced topics rely on the basics and if i can root among/free-form swim about in the deep end the advanced notion will not be completely beyond my grasp, as i will understand that the notions of butterfly swimming/basic concepts are important and know where and how to find them.

i really really hope this idea works. if not i have schaum's, and much thanks for the note!