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. (Make sure you print or otherwise save your work; their is no resultsTracking for this exercise.)

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. If P=Q is logically true in SL (for any SL sentences P and Q), then P and Q are logically equivalent in SL.
This requires a proof by example a general proof.

2. If P>Q is logically true in SL, then the argument with single premise P and conclusion Q is valid in SL.
This requires a proof by example a general proof.

3. If P is logically false in SL, then P&Q is also logically false in SL.
This requires a proof by example a general proof.

4. Two SL sentences P and Q may both be logically indeterminate in SL yet their disjunction PvQ may fail to be logically indeterminate in SL.
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.)