Looking at some exercises in my discrete math book, I came across a few confusing problems.
1) For which sets A, B is it true that A x B = B x A?
2) If there are 2187 functions f: A → B and |B| = 3, what is |A|?
3) Give an example of finite sets A and B with |A|, |B| ≥ 4 and a function f: A→B such that
a) f is neither one-to-one nor onto.
Usually when I see how to begin, or some of the work, it goes a long way in helping me find the answer.
In some cases though, seeing the answer first helps me to see how it was actually solved.
(1) A is empty or B is empty;
(2) A and B are singletons containing the same element;
(3) There exist x ≠ y such that x ∈ A and y ∈ B.
Are these cases exhaustive? What can be said about A x B and B x A in each case?
I'm not in a class yet. I guess I should explain this at the beginning of each post.
I just started going back to college and will be taking a discrete math course. I haven't been in a math class for several years (probably 8) and I knew I would struggle if I didn't practice before. My friend is the same major as me (information technology) and had a discrete math book. I am looking at the exercises from each section to try and learn as much as I can before my class.
I would like to say, though, that reading a course text before the beginning of the course is a very good idea, in my opinion, provided you have enough motivation to go through and understand at least some of the material.
Yeah, unfortunately though, I do kind of pick and choose exercises and do not read everything in each section simply because I just don't have enough time for it. I have been reading probably 30min to 1 hour a day. The one good thing though is this forum, I can check it real quick at work or at home throughout most of the day and add quick replies, which is very helpful so far.
Usually what I post on here are exercises that I couldn't figure out because the examples weren't close enough, or I just don't know enough about the subjects to figure them out myself.
Honestly, I think for these 3 particular problems, it would go a long way just to see the answers, and then I can kind of work backwards to figure out how they were done.
I guess it just depends what type of problem it is, but I don't like to do this for all problems. There is just a sense of satisfaction of figuring out the answer sometimes, but for these I'm having more than usual trouble.