1.4ex V
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 is possible!

1. All pairs of logically true sentences are logically equivalent.
This requires a proof by example a general proof.

 

 

2. No invalid arguments are sound.
This requires a proof by example a general proof.

 

3. Not all unsound arguments are invalid.
This requires a proof by example a general proof.

4. If two sentences logically entail each other, then they are logically equivalent.
This requires a proof by example a general proof.

for printing or saving. (There are no resultsTrack records of this problem because the computer cannot check your work.)