3.5. Compound Boolean Expressions¶
3.5.1. And (&&), Or (), and Not (!)¶
What if you want two things to be true before the body of the conditional is executed? Use &&
as a logical and to join two Boolean expressions and the body of the condition will only be executed only if both are true.
What if you want to go out and your parents say you can go out if you clean your room and do your homework? Run the code below and try different values for cleanedRoom
and didHomework
and see what they have to be for it to print You can go out
.
What if it is okay if only one of two things is true? Use 
as a logical or to join two Boolean expressions and the body of the condition will be executed if one or both are true.
For example, your parents might say you can go out if you can walk or they don’t need the car. Try different values for walking
and carIsAvailable
and see what the values have to be to print You can go out
.
Note
In English, we often use an exclusiveor like in the sentence “do you want to be player 1 or player 2?” where you can’t be both player 1 and player 2. In programming, the oroperator is an inclusiveor which means that the whole expression is true if either one or the other or both conditions are true.
With numerical values, the or () operator is often used to check for error conditions on different ends of the number line, while the and (&&) operator is often used to see if a number is in an range.
Explore how && and  are used with numbers below. Try different values for score like 10 and 110 in the code below.
The not (!
) operator can be used to negate a boolean value. We’ve seen !
before in !=
(not equal). If you use !
in expressions with &&
and 
, be careful because the results are often the opposite of what you think it will be at first. We’ll see examples of this in the next lesson.
The code below says if homework is not done, you can’t go out. Try different values for homeworkDone
.
Note
In Java, ! will be executed before &&, and && will be executed before , unless there are parentheses. Anything inside parentheses is executed first.
3.5.2. Truth Tables¶
The following table (also called a truth table) shows the result for P && Q
when P
and Q
are both expressions that can be true
or false
. An expression involving logical operators like P && Q
evaluates to a boolean
value, true
or false
. As you can see below the result of P && Q
is only true
if both P
and Q
are true
.
P 
Q 
P && Q 

true 
true 
true 
false 
true 
false 
true 
false 
? 
false 
false 
false 
355: The truth table above is missing one result. What is the result of P && Q
when P=true
and Q=false
?
The following table shows the result for P  Q
when P
and Q
are both expressions that can be true
or false
. As you can see below the result of P  Q
is true
if either P
or Q
is true
. It is also true
when both of them are true
.
P 
Q 
P  Q 

true 
true 
true 
false 
true 
? 
true 
false 
true 
false 
false 
false 
356: The truth table above is missing one result. What is the result of P  Q
when P=false
and Q=true
?
 first case
 first case will print if both of the conditions are true and they are.
 second case
 second case will print either of the conditions are false.
357: What is printed when the following code executes and x has been set to 3 and y has been set to 9?
if (x > 0 && (y / x) == 3)
{
System.out.println("first case");
}
else
{
System.out.println("second case");
}
 first case
 first case will print if both of the conditions are true, but the second is not.
 second case
 second case will print if either of the conditions are false and the second one is (6 / 3 == 2).
358: What is printed when the following code executes and x has been set to 3 and y has been set to 6?
if (x > 0 && (y / x) == 3)
{
System.out.println("first case");
}
else
{
System.out.println("second case");
}
 first case
 first case will print if either of the two conditions are true. The first condition is true, even though the second one isn't.
 second case
 second case will print if both of the conditions are false, but the first condition is true.
359: What is printed when the following code executes and x has been set to 3 and y has been set to 6? Notice that it is now an or () instead of and (&&).
if (x > 0  (y / x) == 3)
{
System.out.println("first case");
}
else
{
System.out.println("second case");
}
3.5.3. Short Circuit Evaluation¶
Both &&
and 
use short circuit evaluation. That means that the second expression (on the right of the operator) isn’t necessarily checked, if the result from the first expression is enough to tell if the compound boolean expression is true or false:
If two boolean values/expressions are combined with a logical or (

) and the first expression istrue
, then the second expression won’t be executed, since only one needs to betrue
for the result to betrue
.If two boolean values/expressions are combined with a logical and (
&&
) and the first expression isfalse
, then the second expression won’t be executed. If the first expression isfalse
, the result will befalse
, since both sides of the&&
need to betrue
for the result to betrue
.
 first case
 first case will only print if x is greater than 0 and it is not.
 second case
 second case will print if x is less than or equal to zero or if y divided by x is not equal to 3.
 You will get a error because you can't divide by zero.
 Since the first condition is false when x is equal to zero the second condition won't execute. Execution moves to the else.
3510: What is printed when the following code executes and x has been set to 0 and y to 3?
if (x > 0 && (y / x) == 3)
{
System.out.println("first case");
}
else
{
System.out.println("second case");
}
 first case
 Since x is equal to zero the first expression in the complex conditional will be true and the (y / x) == 3 won't be evaluated, so it won't cause a divide by zero error. It will print "first case".
 second case
 Since x is equal to zero the first part of the complex conditional is true so it will print first case.
 You will get a error because you can't divide by zero.
 You won't get an error because of short circuit evaluation. The (y / x) == 3 won't be evaluated since the first expression is true and an or is used.
3511: What is printed when the following code executes and x has been set to zero and y is set to 3?
if (x == 0  (y / x) == 3)
{
System.out.println("first case");
}
else
{
System.out.println("second case");
}
3.5.4. Programming Challenge : Truth Tables POGIL¶
We encourage you to do this activity as a POGIL (Process Oriented Guided Inquiry Learning) group activity. POGIL groups are selfmanaged teams of up to 4 students where everyone has a POGIL role and works together to solve the problems, making sure that everyone in the team participates and learns.
Explore the following problems with your group:
Draw or print a Venn diagram of 4 intersecting circles. Put the names of the 4 people in your group one in each circle. Write down the age of each person in your group in the circles. If two or more people are the same age, put the age in the intersecting parts of their circles. Write a Boolean expression that compares the age of each person in the group using
==
,<
,>
, and&&
, for example Ada’s age>
Alan’s age&&
Alan’s age==
Grace’s age. Then, ask each person in your group their favorite movie. If two or more people have the same favorite movie, put the movie in the intersecting parts of their circles. Write a Boolean expression that compares the favorite movies in the group using==
,!=
, and&&
, for example Ada’s movie==
Alan’s movie&&
Alan’s movie!=
Grace’s movie. Think of 1 more comparison and write it in the circles and as a Boolean expression. Share the Boolean expressions with the class. (Thank you to Jill Westerlund of Hoover High School and Art Lopez of Sweetwater High School for this activity suggestion).Write the sentence “If it’s sunny, OR if the temperature is greater than 80 and it’s not raining, I will go to the beach.” as a Java if statement using an int variable
temperature
and boolean variablessunny
andraining
. If the conditional is true, print out “Go to the beach!”. So, you will go to the beach on days that it is sunny in any temperature, or you will go to the beach on days when the temperature is over 80 degrees and it’s not raining.Complete a truth table for the if statement that you wrote in #2 with columns for sunny, temperature > 80, raining, and go to the beach.
Write Java code below to test your if statement and try all the values in your truth table to see if you filled it out correctly. You will need test case for each of the 8 rows in your truth table, for example when sunny is true and false, when raining is true or false, and for a value of temperature greater than 80, for example 90, and less than 80, for example 60.
Challenge35truthtables: Test your boolean expression in an if statement below.
3.5.5. Summary¶
Logical operators
!
(not),&&
(and), and
(or) are used with Boolean values.A && B
istrue
if bothA
andB
aretrue
.A  B
istrue
if eitherA
orB
(or both) aretrue
.!A
istrue
ifA
isfalse
.In Java,
!
has precedence (is executed before)&&
which has precedence over
. Parentheses can be used to force the order of execution in a different way.When the result of a logical expression using
&&
or
can be determined by evaluating only the first Boolean operand, the second is not evaluated. This is known as shortcircuit evaluation.
3.5.6. AP Practice¶
Nothing is printed out.

Some of these conditions are true.
First

This is partially correct.
Third

Third cannot be printed out unless First is printed out first.
FirstSecond

Good tracing!
FirstThird

Take another look at the second condition.
3513: Consider the following code segment. What is printed as a result of executing the code segment?
int x = 10;
int y = 5;
if (x % 2 == 0 && y % 2 == 0  x > y)
{
System.out.print("First ");
if (y * 2 == x  y > 5 && x <= 10)
{
System.out.print("Second ");
}
else
{
System.out.print("Third ");
}
}
3.5.7. Boolean Game¶
Try the game below written to practice Booleans. Click on Booleans, look at the color and number in the block and evaluate the boolean expression to choose true or false. Then, check on Compound for an added challenge. We encourage you to work in pairs and see how high a score you can get.