Boolean Operators
There are four boolean logic operators we need to cover: AND, OR, XOR, and NOT. These operators take one or two boolean operands and result in a new boolean value. In Java and many other programming languages, these operators are written as follows:
- AND:
&& - OR (inclusive OR):
|| - XOR (eXclusive OR):
^^ - NOT:
!
AND
If I were to say "it's going to rain and snow tomorrow," then my statement will only be true if it both rains and snows tomorrow. If it only rains, only snows, or doesn't rain or snow, then my statement is false. This is how the boolean AND works.
a && b only results in true if both a and b are both true. If at least
one operand is false, then a && b results in false.
OR and XOR
In English, the word "or" can be used inclusively or exclusively: an inclusive 'or' allows both options to be true, and an exclusive 'or' requires exactly one to be true. For example, consider the following two statements:
- Tomorrow it's at least going to rain or snow. (inclusive)
- Due to the weather, school will either start late or be cancelled entirely. (exclusive)
The first sentence would be true if it both rained and snowed. In the second sentence, the options presented are mutually exclusive; only one can be true.
a || b (inclusive or) always results in true unless both a and b are
false. If both operands are false, then a || b results in false.
a ^^ b (exclusive or) results in true if exactly one of its
operands is true and the other is false. a ^^ b results in false if both
of its operands are true or both are false. You can also say a ^^ b is
true if a isn't equal to b, or false if a and b are the same.
NOT
The NOT operator only applies to one operand. !a results in the opposite of
whatever a is equal to: true if a is false, or false if a is true.
This is how the word "not" is used in English. If I say "I'm not going out
tomorrow," that statement is true if I don't go out and false if I do go out.
Truth Table
Below is a table showing the result of applying each boolean operator to every permutation of true/false values.
| a | b | a && b | a || b | a ^^ b | !a | !b |
|---|---|---|---|---|---|---|
| true | true | true | true | false | false | false |
| true | false | false | true | true | false | true |
| false | true | false | true | true | true | false |
| false | false | false | false | false | true | true |