Topic 2.2 — Boolean Expressions

Goal: write and evaluate boolean expressions using comparison operators and logical operators, and trace code that depends on true/false conditions.

The big idea

A boolean expression is an expression that evaluates to true or false. Boolean expressions control selection (if/else) and repetition (loops).

If you can evaluate booleans correctly, you can predict what code will do.

Two types of building blocks

Comparisons: compare values (like x < y)
Logic: combine booleans (&&, ||, !)

Comparison operators

These compare two values and produce a boolean.

Operator	Meaning	Example
`==`	equal to	`5 == 5` → `true`
`!=`	not equal to	`5 != 2` → `true`
`<`	less than	`3 < 9` → `true`
`<=`	less than or equal	`3 <= 3` → `true`
`>`	greater than	`10 > 4` → `true`
`>=`	greater than or equal	`10 >= 11` → `false`

Logical operators

These combine or flip boolean values.

Operator	Name	Meaning
`&&`	AND	true only if BOTH sides are true
`\|\|`	OR	true if EITHER side is true
`!`	NOT	flips true ↔ false

Truth table basics

// AND (&&)
T && T -> T
T && F -> F
F && T -> F
F && F -> F

// OR (||)
T || T -> T
T || F -> T
F || T -> T
F || F -> F

Short-circuit evaluation (important)

Java may stop early:

For &&, if the left side is false, Java won’t evaluate the right side.
For ||, if the left side is true, Java won’t evaluate the right side.

// If x is 0, this avoids dividing by 0 because the right side won't run:
(x != 0) && (10 / x > 2)

Common mistake: confusing = and ==

= is assignment (sets a variable)
== is comparison (checks equality)

int x = 5;     // assignment
boolean b = (x == 5);  // comparison

Exam mindset

Evaluate from left to right, using precedence: ! then && then ||.
Use parentheses if it helps you reason: (a && b) || c.
Remember short-circuiting can matter when the right side has risks (like divide by zero).

Quick self-check

What values can a boolean expression evaluate to?
What is the difference between && and ||?
What does ! do?
Evaluate: (3 < 5) && (2 == 3)
Why can short-circuiting prevent errors?

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