epdf.pub_the-nuts-and-bolts-of-proofs-third-edition-an-intr

Solutions for the Exercises at
the End of the Sections and
the Review Exercises
WARNING: Vie following solutions for the exercises listed in this book should
be used only as a guide. If you have not read the section ''To the Reader" in the
front of the book, here it is once more!
Learning to construct proofs is like learning to play tennis. It is useful to
have someone teaching us the basics and it is useful to look at someone
playing, but we need to get onto the court and play if we really want to learn.
Therefore, we suggest that you, the reader, set aside a minimum time limit
for yourself to construct a proof without looking at the solution (as a
starting point, you could give yourself one hour and then adjust this limit to
fit your abiUty). If you do not succeed, read only the first few lines of the
proof presented here, and then try again to complete the proof on your own.
If you are not able to do so, read a few more lines and try once more. If you
need to read the entire proof, make sure that you understand it, and after a
few days try the exercise again on your own.
The discussion part of a proof is enclosed in parentheses.
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