3.5 Boolean Expressions

Boolean expressions evaluate to true/false

A Boolean expression evaluates to exactly one of two values: true or false. They're commonly built using relational operators (=, ≠, >, <, ≥, ≤) to compare values, such as `score > 90`. Boolean expressions are used to control program flow, especially in selection (if) and iteration (loop) statements.

Logical operators combine conditions

Logical operators — NOT, AND, OR — combine or invert Boolean expressions. `AND` is true only if both conditions are true; `OR` is true if at least one is true; `NOT` reverses a value. Example: `(age >= 13) AND (age <= 19)` checks if someone is a teenager. These let programs test complex, multi-part conditions.

Boolean expressions drive decisions

In selection statements, the Boolean expression determines which branch executes; in loops, it determines whether iteration continues. Truth tables can be used to trace all possible outcomes of a compound Boolean expression given different input combinations of true/false, helping predict program behavior.

Key terms

Boolean expression

An expression that evaluates to exactly one of two values: true or false.

Relational operator

Operators like =, ≠, >, <, ≥, ≤ used to compare two values.

AND operator

Logical operator that is true only if both connected conditions are true.

OR operator

Logical operator that is true if at least one connected condition is true.

NOT operator

Logical operator that reverses a Boolean value (true becomes false, and vice versa).

Try an AP-style question

x ← 7
r ← (x > 5) AND (x < 10)

What is r?

1. 7
2. false
3. An error
4. true