1.1 Introduction

A discrete structure is defined by a set of axioms. The properties of structure are derived from the axioms as theorems. Such theorems are proved using valid rules of reasoning. The prepositional calculus (Mathematical logic) is concerned with all kinds of reasoning. It has two aspects.

1)       It is the analytic theory of the art of reasoning whose goal is systematic and codify the                             principles of valid reasoning.

2)         It is inter-related with problems relating the foundation of mathematics.

A great mathematician Frege G. (1884-1925) developed the idea regarding a mathematical theory as applied branch of logic.

Every student of engineering should learn logic because principles of logic are valuable to problem analysis, programming, logic designing, code designing and many more.

1.2 Statements or Propositions

A statement is a declarative sentence that is either true or false but not both. The truth or falsity of a statement is called its truth value. The truth value of a true statement is denoted by T and the false statement is denoted by *F. They are also denoted by 1 or 0.

Statements are usually denoted by A, B, C,................ or a, b, c

Examples :

1)         There are 5 days in a week

2)         2 + 5 = 7

3)         y + 3 = 8

4)         It will rain tomorrow

5)         There are 12 months in a year

Examples (2) and (5) are true statements

Example (1) is false statement

In example (3), it's truth value depends upon the value of y. If y is 5 then sentence is true and if y * 5 then sentence is false. Therefore (4) is not a statement.

In example (4), it's truth value cannot be predicted at this moment but it can be definitely determined tomorrow. Hence it is a statement