Introduction

In the previous unit you studied about statements and their truth values. In this unit, we shall discuss ways in which statements can be linked to form a logically valid argument. Throughout your mathematical studies you would have come across the terms ‘theorem’ and ‘proof.

In this, we shall discuss some ideas formalized by the English mathematician Boole and the German logician Frege (1848-1925). These are the different methods used for proving or disproving a statement. As you go through the different types of valid arguments, please try and find connections.

The principle of mathematical induction has a very special place in mathematics because of its simplicity and vast applicability

Objectives

After reading this unit, you should be able to develop in your learners the ability to:

• explain the terms ‘theorem’, ‘proof’ and ‘disproof’;
• describe the direct method and some indirect methods of proof;
• state and apply both forms of the principle of induction