**NOT** (*the first*) **AND NOT** (*the second*)
Using this, you can work **NOT**s through parentheses until eventually they are all applied to relations, and then you can get rid of them. Logically speaking, **NOT** is unnecessary, although you might still find that using it makes a program clearer.
The following section is quite complicated, and can be skipped by the fainthearted!
Try:
```
PRINT 1=2,1<>2
```
which you might expect to give a syntax error. In fact, as far as the computer is concerned, there is no such thing as a logical value: instead it uses ordinary numbers, subject to a few rules.
1. =, <, >, <=, >= and <> all give numeric results: **1** for *true*, and **0** for *false*. Thus the **PRINT** command above printed **0** for **1=2**, which is *false*, and **1** for **1<>2**, which is *true*.
2. In: **IF** *condition* **THEN** ... the condition can be actually any numeric expression. If its value is **0**, then it counts as *false*, and any other value (including the value of **1** that a *true* relation gives) counts as *true*. Thus the **IF** statement means exactly the same as:\
**IF** *condition* <>**0 THEN . . .**
3. **AND, OR** and **NOT** are also number-valued operations.
x ANDy has the value
{
x if y is true (non-zero)
0 (false), if y is false (zero)
xORy has the value
{
1 (true) if y is true (non-zero)
x, if y is false (zero)
NOTx has the value
{
0 (false), if x is true (non-zero)
1 (true), if x is false (zero)
(Notice that *true* means *non-zero* when we're checking a given value, but it means **1** when we're producing a new one.)
Read through the chapter again in the light of this revelation, making sure that it all works.
In the expressions **x AND y**, **x OR y** and **NOT x**, *x* and y will usually take the values **0** and **1** for *false* and *true*. Work out the ten different combinations (four for **AND**, four for **OR** and two for **NOT**) and check that they do what the chapter leads you to expect them to do.
Try this program:
```
10 INPUT a
20 INPUT b
30 PRINT (a AND a>=b)+(b AND
a