Chapter 12 – Conditions

AND, OR and NOT

We saw in Chapter 2 how an IF statement takes the form:

IF condition ...

Apart from expressions that generate true (1) or false (0) results, the conditions there, were the relations (=, <, >, <=, >= and <>), which compare two numbers or two strings. You can also combine several of these, using the logical operations, AND, OR and NOT.

One relation AND another relation is true whenever both relations are true, so you could have a line like:

IF a$="yes" AND x>0 THEN PRINT x

in which x only gets printed if a$="yes" and x>0. The syntax here is so close to English that it hardly seems worth spelling out the details. As in English, you can join lots of relations together with AND, and then the whole lot is true if all the individual relations are.

One relation OR another is true whenever at least one of the two relations is true. (Remember that it is still true if both the relations are true; this is not always implied in English).

The NOT relationship turns things upside down. The NOT relation is true whenever the relation is false, and false whenever it is true!

Logical expressions, can be made with relations and AND, OR and NOT, just as numerical expressions can be made with numbers and +, - and so on; you can even put them in parentheses if necessary. They have priorities in the same way as the usual operations +, -, *, / and ↑ do: OR has the lowest priority, then AND, then NOT, then the relations, and the usual operations.

NOT is really a function, with an argument and a result, but its priority is much lower than that of other functions. Therefore its argument does not need parentheses unless it contains AND or OR (or both). NOT a=b means the same as NOT (a=b) (and the same as a<>b, of course).

<> is the negation of = in the sense that it is true if, and only if, = is false. In other words:

a<>b is the same as NOT a=b

and also:

NOT a<>b is the same as a=b

Persuade yourself that >= and <= are the negations of < and > respectively: thus you can always get rid of NOT from in front of a relation by changing the relation.

Also:

NOT (a first logical expression AND a second)

is the same as:

NOT (the first) OR NOT (the second)

and:

NOT (a first logical expression OR a second)

is the same as: