Unit 3: Boolean Expressions and if Statements

Key Concepts

• Boolean Expressions: Expressions that evaluate to true or false.
• Relational Operators: ==, !=, <, >, <=, >=.
• Logical Operators: && (AND), || (OR), ! (NOT).
• Conditional Statements: if, else if, else.
• Nested Conditionals: Using conditionals inside other conditionals.
• De Morgan's Laws: Rules for simplifying logical expressions.

Example Code: Advanced Boolean Expressions

// Example: Advanced Boolean Expressions and Complex Conditionals
public class AdvancedBooleanExample {
    public static void main(String[] args) {
        // Complex boolean expressions
        int score = 85;
        boolean isPassing = score >= 60;
        boolean isHonors = score >= 90;
        boolean hasPerfectAttendance = true;
        
        // Using De Morgan's Laws
        boolean notPassing = !isPassing;
        boolean notHonors = !isHonors;
        
        // Complex conditional logic
        if (isHonors && hasPerfectAttendance) {
            System.out.println("Student qualifies for highest honors!");
        } else if (isPassing && hasPerfectAttendance) {
            System.out.println("Student qualifies for attendance award.");
        } else if (isPassing) {
            System.out.println("Student is passing.");
        } else {
            System.out.println("Student needs improvement.");
        }
        
        // Ternary operator example
        String grade = isHonors ? "A" : (isPassing ? "C" : "F");
        
        // Short-circuit evaluation
        boolean result = isPassing || (score > 100); // Second condition never evaluated if isPassing is true
        
        // Print results
        System.out.println("Grade: " + grade);
        System.out.println("Short-circuit result: " + result);
    }
}
              

Boolean Expressions and Logical Operators

Common Boolean Operators:

Boolean Expression Examples:

// Basic boolean expressions
boolean isAdult = age >= 18;
boolean isTeenager = age >= 13 && age <= 19;
boolean isChild = age < 13;

// Complex boolean expressions
boolean canVote = age >= 18 && isCitizen;
boolean canDrive = age >= 16 || hasSpecialPermit;
boolean isWeekend = day == "Saturday" || day == "Sunday";

// Using NOT operator
boolean isNotAdult = !isAdult;
boolean isNotWeekend = !isWeekend;
              

Short-Circuit Evaluation:

// && short-circuits if first condition is false
if (x != 0 && y / x > 2) {
    // Safe division because x != 0 is checked first
}

// || short-circuits if first condition is true
if (name == null || name.length() == 0) {
    // Safe length check because null is checked first
}
              

Boolean Expression Tips:

• Use parentheses to clarify complex expressions
• Take advantage of short-circuit evaluation
• Use meaningful variable names for boolean values
• Consider De Morgan's Laws for simplifying expressions
• Be careful with floating-point comparisons

Common Pitfalls and Debugging Tips

Common Mistakes:

• Assignment vs. Comparison: Using = instead of ==

  
  if (x = 5) {  // Wrong! Assigns 5 to x
  if (x == 5) { // Correct! Compares x with 5
                    

• Floating-Point Comparison: Using == with doubles

  
  double x = 0.1 + 0.2;
  if (x == 0.3) {  // Wrong! Might be false due to precision
  if (Math.abs(x - 0.3) < 0.0001) {  // Correct! Uses tolerance
                    

• String Comparison: Using == instead of equals()

  
  String s1 = "Hello";
  String s2 = new String("Hello");
  if (s1 == s2) {  // Wrong! Compares references
  if (s1.equals(s2)) {  // Correct! Compares content
                    

Debugging Tips:

• Use System.out.println() to print boolean values
• Break complex expressions into smaller parts
• Use parentheses to clarify operator precedence
• Test edge cases (null, zero, empty strings)
• Use truth tables to verify complex logic

AP Exam Tips:

• Know operator precedence rules
• Understand short-circuit evaluation
• Be able to evaluate complex boolean expressions
• Know when to use equals() vs ==
• Understand De Morgan's Laws

AP Exam-Style Practice Problems

int x = 5;
int y = 10;
boolean result = (x > 3) && (y < 15) || (x + y == 20);
System.out.println(result);
                

int x = 0;
boolean result = (x != 0) && (10 / x > 2);
System.out.println(result);
                

String s1 = "Hello";
String s2 = new String("Hello");
System.out.println(s1 == s2);
System.out.println(s1.equals(s2));
                

int age = 16;
boolean hasLicense = true;
boolean hasParent = false;
boolean canDrive = (age >= 16 && hasLicense) || (age >= 15 && hasParent);
System.out.println(canDrive);
                

Practice Problems

1. Write a program that checks if a number is positive, negative, or zero.
2. Write a program that determines if a year is a leap year.
3. Write a program that checks if a user is eligible to vote (age >= 18).
4. Write a program that uses nested conditionals to determine the grade based on a score.
5. Write a program that checks if a number is divisible by both 3 and 5.
6. Create a program that determines if a triangle is valid based on its side lengths.
7. Write a program that checks if a string is a palindrome using boolean expressions.
8. Create a program that determines if a number is prime using boolean logic.

Interactive Code Playground

Try out your own boolean expressions and conditional statements here!

Note: This is a simulated environment. For actual Java code execution, please use an IDE or online Java compiler.

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