due March 5th, 1999

INSTRUCTIONS: This assignment is due March 5th 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.

Any axiom may be used. Lower numbered theorems may be used in the proof of a higher numbered theorem.

- Give a full dress proof that ( 3.76 d)) using
proof technique 4.1.
SOLUTION

Hence by derived inference rule for number 2, .

- Give a full dress proof of modus ponens ( 3.77), i.e. using the Deduction Theorem (4.4).
SOLUTION

Assume .

Hence by TRANSITIVITY 3 times and EQUANIMITY . Hence by the Deduction Theorem it follows that .

- Give a full dress proof that using Proof
by Cases (4.5). You are allowed to use theorems upto and including Theorem 3.40.
SOLUTION

gives

Subs . TRANSITIVITY twice and EQUANIMITY gives that .

Now gives

Subs

*p*:=*false*. TRANSITIVITY three times and EQUANIMITY gives that .Hence by Proof by Cases it follows that .