Yet More Informal Proofs
Write out proofs for each of the following propositions. This work is yours and in your own words. So, the computer can give only limited help.
Try to follow the methods developed in earlier problems.
You may want to begin with a supposition about an arbitrary member
of a class and prove that a claim holds in general. In other cases,
the proposition to prove only requires an example. How do you tell the
difference? (a) The general case will ask you to prove a proposition
about all or any member of a class. Begin with a supposition about an
arbitrary member, and show it must satisfy the claim. (b) The cases
for which an example is sufficient will ask you to prove a proposition
that some sort of thing is possible. Construct an example to show it