CS 501  Homework # 3

Problem 1.

In propositional logic, elementary propositions may be combined
by five logical connectives:

P <--> Q   : P if and only if Q
P --> Q    : If P then Q   (or P implies Q)
P & Q      : P and Q
P v Q      : P or Q
~ P        : not P

The truth tables for these logical connectives are:

P      Q  |  P <--> Q  |  P --> Q  |  P & Q  | P v Q | ~ P
          |            |           |         |       |
T      T  |      T     |     T     |    T    |   T   |   F 
T      F  |      F     |     F     |    F    |   T   |   F 
F      T  |      F     |     T     |    F    |   T   |   T 
F      F  |      T     |     T     |    F    |   F   |   T 

Logical expressions involving these connectives may combine 
many connectives applied according to the following operation
hierarchy:

all ~ are applied first
next all & are applied
next all v are applied
next all --> are applied
finally all <--> are applied

Parentheses may be used to override this hierarchy.
A Logical expression which always evaluates to true is called
a tautology. Example:  (P --> Q) <--> (~P v Q) is a tautology,
because it is true for all possible combinations of true/false 
values of P and Q.

Write a program that tells you if the expression entered is a
tautology or not. Assume that you have no more than three 
propositional symbols in your expressions -- call them P, Q, R. 
You must use the linked list implementation of the data
structures needed.

Submit an extended "design" description of your program (data 
structures and methods used), as well as disk, hardcopy, and 
example runs.

Problem 2.

Given the following postorder and inorder traversals of a binary 
tree, draw the tree:
   
   Postorder:  A   B   C   D   E   F   I   K   J   G   H

   Inorder:    C   B   A   E   D   F   H   I   G   K   J

Explain your answer in a systematic and recursive fashion.