Unit 2: Boolean Logic

Table of Contents

1. Boolean Logic
2. Logical Operators
   1. AND
   2. OR
   3. NOT
   4. XOR
3. Relational Operators

Boolean Logic

Boolean logic, named after mathematician George Boole, is how we form conditional statements in programming. This is important because sometimes we only want certain code to run if certain conditions are met.

Logical Operators

Boolean logic in programming revolves around three key components: AND, OR, and NOT. These operators can compare multiple booleans together to see if a statement is true or false. In Java, these operators use different symbols.

AND

The AND operator in Java is &&, and separates two booleans. It checks to see if the two boolean statements are both true. If they are both true, then the complete boolean statement would be true.

boolean isRaining = true;
boolean isCloudy = true;

System.out.println(isRaining && isCloudy); // prints true

However, if one or both of the booleans are false, then the whole boolean statement would be false.

boolean isRaining = true;
boolean isCloudy = false;

System.out.println(isRaining && isCloudy); // prints false

Truth Table

var1	var2	var1 && var2
true	true	true
true	false	false
false	true	false
false	false	false

Note: The logical AND (&&) is different from the bitwise AND (&)!

OR

The OR operator in Java is ||, and checks to see if at least one of the booleans statements is true. If both are true, then the complete boolean statement would be true.

boolean isRaining = true;
boolean isCloudy = false;

System.out.println(isRaining || isCloudy); // prints true

Only if both statements were false, then the complete boolean statement would return false.

boolean isRaining = false;
boolean isCloudy = false;

System.out.println(isRaining || isCloudy); // prints false

Truth Table

var1	var2	var1 || var2
true	true	true
true	false	true
false	true	true
false	false	false

Note: The logical OR (||) is different from the bitwise OR (|)!

NOT

The NOT operator in Java is !, and is a little bit different from the AND and OR operators. Instead of comparing two different boolean statements, the NOT operator simply gives the opposite of a boolean statement. In this example, if the NOT operator is used, the print statement would print true.

boolean isRaining = false;

System.out.println(!isRaining); // prints true

Truth Table

var	!var
true	false
false	true

Note that you can combine operators however you wish. Just make sure that you use parentheses to make it clear in what order you want the boolean expressions to be evaluated!

XOR

There is another logical operator called XOR (exclusive OR), which is ^. It is not commonly used, but it’s nice to know for reference. The result of an XOR is true only if exactly one value is true.

Truth Table

var1	var2	var1 ^ var2
true	true	false
true	false	true
false	true	true
false	false	false

Relational Operators

As their name suggests, relational operators deal with the relationships between two values.

Relational Operator	In words	Example
>	greater than	5 > 3 is true
<	less than	5 < 3 is false
>=	greater than or equal to	5 >= 5 is true
<=	less than or equal to	3 <= 2 is false
==	equal to	5 == 5 is true
!=	not equal to	5 != 5 is false

The greater >, <, >=, and <= operators are used with numbers. == and != can be used with numbers or other values. Note that the equality and inequality operators can be tricky because technically they check if two values are located in the same place in memory. We will later learn that even if the value of a variable is identical to another, it may not be “equal” using the equality operator.