SELECTIONS - Introduction to Java Programming: Comprehensive Version - page 95

15 if (number % 2 == 0 || number % 3 == 0 )
16 System.out.println(number + " is divisible by 2 or 3." );
17
18 if (number % 2 == 0 ^ number % 3 == 0 )
19 System.out.println(number +
20

or

exclusive or

" is divisible by 2 or 3, but not both." );

21 }
22 }

Enter an integer: 4
4 is divisible by 2 or 3.
4 is divisible by 2 or 3, but not both.

Enter an integer: 18
18 is divisible by 2 and 3.
18 is divisible by 2 or 3.

(number % 2 == 0 && number % 3 == 0) (line 12) checks whether the number is
divisible by both 2 and 3 . (number % 2 == 0 || number % 3 == 0) (line 15) checks
whether the number is divisible by 2 or by 3 . (number % 2 == 0 ^ number % 3 == 0) (line
18) checks whether the number is divisible by 2 or 3 , but not both.

Caution
In mathematics, the expression

1 <= numberOfDaysInAMonth <= 31

is correct. However, it is incorrect in Java, because 1 <= numberOfDaysInAMonth is
evaluated to a boolean value, which cannot be compared with 31 . Here, two operands
(a boolean value and a numeric value) are incompatible . The correct expression in
Java is

incompatible operands

( 1 <= numberOfDaysInAMonth) && (numberOfDaysInAMonth <= 31 )

Note
De Morgan's law, named after Indian-born British mathematician and logician Augustus
De Morgan (1806-1871), can be used to simplify Boolean expressions. The law states:

De Morgan's law

!(condition1 && condition2) is the same as
!condition1 || !condition2
!(condition1 || condition2) is the same as
!condition1 && !condition2

For example,
! (number % 2 == 0 && number % 3 == 0 )

can be simplified using an equivalent expression:
(number % 2 != 0 || number % 3 != 0 )

As another example,
!(number == 2 || number == 3 )

is better written as
number != 2 && number != 3