Description

Introduction

We will use an updated version of logic.py that offers additional features. Make sure you download the new version from CatCourses and place it in your working directory. The version from last week will not allow you to solve this exercise.

Originally, to create a truth table for the expressions p∧q, and p∨q, we had to do the following:

myTable = TruthTable([’p’, ’q’], [’p and q’, ’p or q’])

We no longer have to provide the first parameter, so now we call:

myTable = TruthTable([’p and q’, ’p or q’])

The library goes through the list of propositions and figures out the variable names for us.

To solve the questions in this exercise, you have to examine the structure of the truth table built by the object TruthTable. This can be done by accessing the data member table. For example, the following lines extract the truth table and print it to the screen.

myTable = TruthTable([’p and q’, ’p or q’]) a = myTable.table print(a)

The truth table is represented by a list of lists, with each sublist representing a row in the truth table. To solve the following questions, it will be useful for you to first examine its structure and interact with it from the command line (e.g., to read out its elements).

1

Tautologies, contingencies and contradictions

Write a program that reads a logic expression from the keyboard and prints to the screen whether the expressions is a tautology, a contingency, or a contradiction. Your code should work for expressions with an arbitrary number of variables (i.e., do not assume the expression has only two variables and therefore the truth table has just four rows).

Optional – Logical Equivalences

This question will not give you extra credit, but you are invited to try it out if you finish early. Write a program that reads and arbitrary number of logical expressions and determines if they are all logically equivalent to each other.