Topic 3.5 Notes – Boolean Expressions

1. What Boolean Values Are

A Boolean value can only be one of two things: true or false. Nothing in between.

Programs use Boolean values to decide what to do. Whenever you see an IF statement or a loop condition, it’s checking a Boolean expression.

A Boolean expression is any expression that evaluates to either true or false.

Two big categories create Boolean values:

• Relational operators → compare values
• Logical operators → combine or modify Boolean values

If you see a condition on a quiz, your job is simple: figure out whether it becomes true or false.

2. Relational Operators Compare Two Values

Relational operators compare two variables, expressions, or values. The result is always a Boolean.

The Six You Must Know

These are exactly the ones on the AP reference sheet:

• = equal to
• ≠ not equal to
• > greater than
• < less than
• ≥ greater than or equal to
• ≤ less than or equal to

Each side can be:

• A number (7)
• A variable (score)
• An expression (x + 3)

How to Evaluate One

Example:

x ← 8
y ← 10
x + 2 ≥ y

Step-by-step thinking:

1. Evaluate arithmetic first
   x + 2 → 8 + 2 → 10
2. Compare
   10 ≥ 10
3. Decide
   That’s true

Two common mistakes:

• Forgetting that = means comparison in pseudocode (assignment uses ←)
• Forgetting that ≥ and ≤ include equality

Boundary cases show up a lot on multiple choice questions.

3. Logical Operators Combine or Modify Boolean Values

Logical operators work only on Boolean values or Boolean expressions. They also produce a Boolean.

The three you need:

• NOT
• AND
• OR

NOT

NOT condition

It flips the value.

• NOT true → false
• NOT false → true

If you see NOT(score = 90), evaluate the inside first, then reverse it.

AND

condition1 AND condition2

True only if both conditions are true.

Think of it as a checklist. If one fails, the whole thing is false.

OR

condition1 OR condition2

True if:

• The first is true
• The second is true
• Both are true

It’s only false when both are false.

Here’s a quick truth summary you should recognize instantly:

And for NOT:

If you ever blank during a test, rebuild the logic from this pattern.

4. Evaluating Combined Boolean Expressions

On quizzes and the AP exam, conditions are usually layered.

Example:

(a > 3) AND (b ≤ 12)

How to evaluate:

1. Evaluate each relational comparison first.
   Each becomes true or false.
2. Apply NOT if present.
3. Combine using AND or OR.

Example:

a ← 4
b ← 15
(a > 3) AND (b ≤ 12)

• a > 3 → true
• b ≤ 12 → false
• true AND false → false

Final answer: false

Important rule from the reference sheet:

The operand of a logical operator must be:

• A Boolean value
• Or a Boolean expression

You cannot write 5 AND 7. Each side must evaluate to true or false.

Students often lose points by misreading grouped conditions. Slow down and evaluate one piece at a time.

5. Why Boolean Expressions Matter in Programs

Boolean expressions control:

• Whether an IF statement runs
• Which branch of code executes
• Whether a loop continues

Because programs execute statements in order, changing a Boolean condition can completely change the output.

When the AP gives you a code segment and asks what prints, almost always you’re tracing Boolean conditions somewhere.