due January 29th, 1999

INSTRUCTIONS: This assignment is due January 29th 1999, in class. Groups may hand in a single assignment paper. The maximum group size is 4.

The assignments must have the name and York number of all group members listed at the top of the paper.

- Using truth tables show that is a tautology.
SOLUTION:

So since is

*T*(or*true*) in all states, it is a tautology. - Fill in the missing details to make the following a full dress proof that .
SOLUTION:

By Metatheorem which says if since and we have .

By TRANSITIVITY 4 times and hence by EQUANIMITY .

- Give a full dress proof that . You may use any of the axioms given in Chapter
3.
SOLUTION:

Now , and by TRASITIVITY 3 times, and so by EQUANIMITY.