CS 253  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.

Must submit all .java files and outputs -- at least two test
 cases, for tautology, and not a tautology.


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.