I have been following Velleman's How to prove it and working through it on my own. I am working full time now so I can only study after work without any other help. It's been going fairly ok until I started studying existence and uniqueness proof for sets.
I simply cannot grasp the strategy at all. I have the solution to every problem, but every problem I have encountered involves assuming one set to be identical to another, numerous comments on this site mentioned that knowing what to assume comes with practise, but this is the problem - every single problem I come across in this book starts off impossible and I cannot make any progress that grants me experience. The book also offers no strategy at all apart from noting the three equivalent forms of ext. and uniq. proof (in fact, not even any useful example on proving such sets except a pretty easy one).
I am also suffering huge anxiety from this; at one point I was stuck at a question for a month (I have since given it up), and despite asking for help on this forum, I cannot even fully understand the solutions offered. I am so anxious that at one point I found myself panting heavily even when I merely set sight on a problem.
So may I ask for help on the following please:
Good reference book with abundant exercises + solutions on existence and uniqueness proof on sets
How do I cope with the anxiety?
Good strategy to solving existence and uniqueness proofs/reference that discusses such matters
Thank you so much!