## 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: **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 AND y has the value	{	x if y is true (non-zero)
		0 (false), if y is false (zero)

x OR y has the value	{	1 (true) if y is true (non-zero)
		x, if y is false (zero)

NOT x 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 An expression using **AND** or **OR** like this is called a *conditional expression*. An example using **OR** could be: ``` price=price_less_tax*(1.15 OR v$="zero rated") ``` Notice how **AND** tends to go with addition (because its default value is **0**), and **OR** tends to go with multiplication (because its default value is **1**). You can also make string valued conditional expressions, but only using **AND**.

x$ AND y has the value	{	x$ if y is non-zero
		"" if y is zero

So it means **x$ if y** (else the empty string). Try this program, which inputs two strings and puts them in alphabetical order: ``` 10 INPUT "Type in two strings"'a$,b$ 20 IF a$>b$ THEN c$=a$:a$=b$:b$=c$ 30 PRINT a$;" ";("<" AND a$ b OR c ``` nor is it ``` IF a<>b OR a<>c ```