Logical Expressions

Logical Expressions

The IF statements and the DO WHILE statements of the previous chapters could only ask simple questions, like COUNT < 10 or HUE >= 16. Often simple questions like these are not enough. This chapters discusses ways to ask more complicated questions.

Chapter Topics:

• Relational Expressions (review)
• Logical Expressions
• AND Operator in QBasic
• Checking that a number is in range
• Syntax of Logical Expressions
• OR Operator in QBasic
• Comparison between AND and OR

QUESTION:

You have decided to bake some cookies (much cheaper than getting them at the Mall.) An interesting cookie recipe calls for 4 cups of flour and 1 cup of sugar. You look in your supplies and find 3 cups of flour and 2 cups of sugar.
Can you bake cookies with the supplies that you have?

The question about whether you have enough supplies has two parts:

You need at least 4 cups of flour   AND   You need at least 2 cups of sugar

Since you do not have enough flour, you don't have enough supplies.

QUESTION:

What if you had 9 cups of flour and 1 cup of sugar. Now could you follow the recipe?

In order to bake cookies two things must be true:

• You must have at least 4 cups of flour.
• You must have at least 2 cups of sugar.

If one of these requirements is false, then you do not have enough ingredients. A QBasic program that follows this logic is:

' Cookie Ingredients Checker
'
PRINT "How much flour do you have"
INPUT FLOUR
PRINT "How much sugar do you have"
INPUT SUGAR
'
IF FLOUR >= 4 AND SUGAR >= 2 THEN
  PRINT "You have enough ingredients"
ELSE
  PRINT "You do not have enough"
END IF
'
END

The IF statement is asking a question with two parts:

IF FLOUR >= 4 AND SUGAR >= 2 THEN
   ----------     ----------
   flour part     sugar part

Each one of these parts is a relational expression (as in the previous chapters.) A relational expression looks at two numbers and gives you TRUE or FALSE.

QUESTION:

Say that you enter 9 for FLOUR and 1 for SUGAR. What answer (TRUE or FALSE) does each of the parts give you?

               
FLOUR >= 4  ________________

SUGAR >= 2  ________________

Here is the program again:
' Cookie Ingredients Checker ' PRINT "How much flour do you have" INPUT FLOUR PRINT "How much sugar do you have" INPUT SUGAR ' IF FLOUR >= 4 AND SUGAR >= 2 THEN PRINT "You have enough ingredients" ELSE PRINT "You do not have enough" END IF ' END For you to have enough ingredients, both relational expressions must be TRUE. This is the role of the AND between the two relational expressions. The AND requires that both
FLOUR >= 4 and
SUGAR >= 2 are true before the entire question is true. The entire question must be true in order for the true branch to execute.
The two part question is an example of a logical expression. A logical expression looks at the TRUE and FALSE answers of relational expressions. It will itself give you a TRUE or FALSE.

QUESTION:

Look at the program. How will the monitor screen look if the user types 6 for FLOUR and 4 for SUGAR?

When execution gets to the IF statement, it finds that

FLOUR >= 4   —— true, because 6 >= 4

and

SUGAR >= 2    —— true, because 4 >= 2

Since both sides are true, the two part question gives us TRUE.
AND is used in a logical expression to insist that there is a TRUE on both sides:

this side must be true  AND this side must be true

If both sides are true, the entire AND expression is true. If either side (or both) are false, the entire AND expression is false. AND is called a logical operator because it combines two true/false values into a single true/false value.
A compact way of saying what AND does is:

• true AND true = true     -- This is the only true.
• false AND true = false
• true AND false = false
• false AND false = false

AND is used to check that every requirement is met.

QUESTION:

Look at the logical expression:

FLOUR >= 4 AND SUGAR >= 2 

What will the expression give us if FLOUR is 2 and SUGAR is 0?