SE-561

Math Foundations of Software Engineering

Homework Assignment 1 (Due Thursday, Oct. 5)

    1. Prove the following sequents:

a.  q --> (p-->r), ~r, q |- ~p
b.  p |- q --> (p /\ q)
c.  p --> q |- ((p /\ q) --> p) /\ (p --> (p /\ q))
d.  p \/ (p /\ q) |- p
e.  (p /\ q) \/ (p /\ r) |- p /\ (q \/ r)
f.   ~p --> p |- p
g.  p /\ q |- ~(~p \/ ~q)
h.  |- ((p --> q) --> q) --> ((q --> p) --> p)

   2.  Draw the parse trees for the following formulas:

          a. (p /\ q) --> (~r \/ (q --> r))
          b. (p --> q) /\ (~r --> (q \/ (~p /\ r)))