2.6 Comparing Boolean Expressions

1. Exam Points

• Two Boolean expressions are equivalent if they have the same value in all cases.
• De Morgan’s law:
  • !(a && b) is equivalent to !a || !b
  • !(a || b) is equivalent to !a && !b
• Compare object references using == or !=.
• Compare object references using the equals method.
• Compare an object reference and null using == and !=
• Note: Do not access members on a null object.

2. Knowledge Points

(1) Comparing Boolean Expressions

• Two Boolean expressions are equivalent if they evaluate to the same value in all cases.
  • Example:
    • ! ( a && b ) is equivalent to !a || !b
    • !( x > y && x > z ) is equivalent to !(x > y) || !(x > z)
• De Morgan’s law can be applied to Boolean expressions to create equivalent Boolean expressions.
• Under De Morgan’s law:
  • !(a && b) is equivalent to !a || !b
  • !(a || b) is equivalent to !a && !b
  • !(a && b && c) = !a || !b || c
  • !(a || b || c) = !a && !b && c

(2) Compare Variables of Reference Types

• Two different variables can hold references to the same object.
  • Example 1: d1 and d2 refer to different objects.

  Dog d1 = new Dog() ;
  Dog d2 = new Dog() ;
  

  • Example 2: d1 and d2 refer to the same object

  Dog d1 = new Dog() ;
  Dog d2 = d1 ;
  

• Object references can be compared using == and != .
  • Example 1:
    

  Dog d1 = new Dog() ;
  Dog d2 = new Dog() ;
  boolean result = d1 == d2;
  // result is false since d1 and d2 refer to two different objects.
  

  • Example 2:
    

  Dog d1 = new Dog() ;
  Dog d2 = d1 ;
  boolean result = d1 == d2;
  // result is true since d1 and d2 refer to the same object.
  

• An object reference can be compared with null, using == or !=, to determine if the reference actually references an object.
  • Example:
    

  Dog d1 = null;
  Dog d2 = new Dog();
  
  System.out.println(d1 == null); // true
  System.out.println(d2 == null); // false
  System.out.println(d2 != null); // true
  

  • Note: Do not access instance variables or methods of a null object, it will lead to NullPointerException.

(3) Ways to Compare Two Objects

• Two ways to compare two object references:
  • Compare two object references using == and !=
  • Compare two object references using the equals() method
• Classes often define their own equals method, which can be used to specify the criteria for equivalency for two objects of the class.
• The equivalency of two objects is most often determined using attributes from the two objects.
• (AP Exam Exclusion: overriding the equals() method)

3. Exercises

• Practice
• Solution