The proofs involving Cartesian products of sets seemed a little more difficult. It seems as if keeping all the different elements straight will be quite difficult. However, the idea is fairly straight forward. One need take the variables separately and remember what sets the individuals are elements of. Of course, with practice, it will continue to become more clear.
I find the counterexamples to be very useful. I was in a debate earlier today, the opposing side used a generalization in a certain domain. I thought of a counterexample that disproved their statement. Though the counterexample did not prove their whole argument as false (because debates are much more subjective than mathematics) I felt logically validated for my use of a counterexample.
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