2.3 Basics of logic

This section introduces two fundamental concepts of mathematical logic: Boolean algebra (after George Boole, one of the founders of mathematical logic) and logical deduction.

The building blocks of logic are statements. Statements are simple declarative sentences which are either true or false, but cannot be both at once. This is analogous to set theory where an element either belongs to a set or not. As with the case of set theory, there is a growing interest in finding ways to deal with fuzzy logic statements ( may be true , could be false , etc.).

Instead of taking numerical values, Boolean quantities take only two values: 1 (for true) or 0 (for false), also represented as T and F, respectively. For example, the statement The earth is flat , would be true if the earth were flat, but in fact this sentence is false. This statement is a constant statement; that is there are no variables in it. However, computer programming normally requires the use of statements which have variable values. As an example suppose that P( x) corresponds to the proposition x is an even number . As it stands, it is not possible to know whether this is true or not. But if one sets x = 2, then the statement is true; conversely, by setting x = 3, then it is false.

As with the case of set theory, it is often inconvenient to write logical statements...