Understanding Boolean Logic in Python 3

Updated on February 1, 2021
Understanding Boolean Logic in Python 3


The Boolean data type can be one of two values, either True or False. We use Booleans in programming to make comparisons and to determine the flow of control in a given program.

Booleans represent the truth values that are associated with the logic branch of mathematics, which informs algorithms in computer science. Named for the mathematician George Boole, the word Boolean always begins with a capitalized B. The values True and False will also always be with a capital T and F respectively, as they are special values in Python.

In this tutorial, we’ll go over what you’ll need to understand how Booleans work in Python, and explore comparison operators, logical operators, and truth tables.


You should have Python 3 installed and a programming environment set up on your computer or server. If you don’t have a programming environment set up, you can refer to the installation and setup guides for a local programming environment or for a programming environment on your server appropriate for your operating system (Ubuntu, CentOS, Debian, etc.)

Comparison Operators

In programming, comparison operators are used to compare values and evaluate down to a single Boolean value of either True or False.

Info: To follow along with the example code in this tutorial, open a Python interactive shell on your local system by running the python3 command. Then you can copy, paste, or edit the examples by adding them after the >>> prompt.

The table below is of Boolean comparison operators.

Operator What it means
== Equal to
!= Not equal to
< Less than
> Greater than
<= Less than or equal to
>= Greater than or equal to

To understand how these operators work, let’s assign two integers to two variables in a Python program:

x = 5
y = 8

In this example, since x has the value of 5, it is less than y which has the value of 8.

Using those two variables and their associated values, let’s go through the operators from the table above. In our program, we’ll ask Python to print out whether each comparison operator evaluates to either True or False. To help us and other humans better understand this output, we’ll have Python also print a string to show us what it’s evaluating.

x = 5
y = 8

print("x == y:", x == y)
print("x != y:", x != y)
print("x < y:", x < y)
print("x > y:", x > y)
print("x <= y:", x <= y)
print("x >= y:", x >= y)

When we run this program, we’ll receive the following output.

x == y: False x != y: True x < y: True x > y: False x <= y: True x >= y: False

Following mathematical logic, in each of the expressions above, Python has evaluated:

  • Is 5 (x) equal to 8 (y)? False
  • Is 5 not equal to 8? True
  • Is 5 less than 8? True
  • Is 5 greater than 8? False
  • Is 5 less than or equal to 8? True
  • Is 5 not less than or equal to 8? False

Although we used integers here, we could substitute them with float values.

Strings can also be used with Boolean operators. They are case-sensitive unless you employ an additional string method.

Here are how strings are compared with Boolean operators in practice:

Sammy = "Sammy"
sammy = "sammy"

print("Sammy == sammy: ", Sammy == sammy)

The output for the program above returns the following.

Sammy == sammy: False

The string "Sammy" above is not equal to the string "sammy", because they are not identical; one starts with an upper-case S and the other with a lower-case s. But, if we add another variable that is assigned the value of "Sammy", then they will evaluate to equal:

Sammy = "Sammy"
sammy = "sammy"
also_Sammy = "Sammy"

print("Sammy == sammy: ", Sammy == sammy)
print("Sammy == also_Sammy", Sammy == also_Sammy)

After running the program above, we’ll get the following output. This indicates that as long as the string is absolutely identical (including case), then they will evaluate as equal from a Boolean logic perspective.

Sammy == sammy: False Sammy == also_Sammy: True

You can also use the other comparison operators including > and < to compare two strings. Python will compare these strings lexicographically using the ASCII values of the characters.

We can also evaluate Boolean values with comparison operators:

t = True
f = False

print("t != f: ", t != f)

The program above will return the following.

t != f: True

As indicated in the output above, the code we wrote evaluated that True is not equal to False.

Note the difference between the two operators = and ==.

x = y	# Sets x equal to y
x == y	# Evaluates whether x is equal to y

The first, = is the assignment operator, which will set one value equal to another. The second, == is a comparison operator which will evaluate whether two values are equal.

Logical Operators

There are three logical operators that are used to compare values. They evaluate expressions down to Boolean values, returning either True or False. These operators are and, or, and not and are defined in the table below.

Operator What it means Example
and True if both are true x and y
or True if at least one is true x or y
not True only if false not x

Logical operators are typically used to evaluate whether two or more expressions are true or not true. For example, they can be used to determine if the grade is passing and that the student is registered in the course. If both of these cases are true, then the student will be assigned a grade in the system. Another example would be to determine whether a user is a valid active customer of an online shop based on whether they have store credit or have made a purchase in the past 6 months.

To understand how logical operators work, let’s evaluate three expressions:

print((9 > 7) and (2 < 4))	# Both original expressions are True
print((8 == 8) or (6 != 6))	# One original expression is True
print(not(3 <= 1))			# The original expression is False
True True True

In the first case, print((9 > 7) and (2 < 4)), both 9 > 7 and 2 < 4 evaluate to True since the and operator was being used.

In the second case, print((8 == 8) or (6 != 6)), since 8 == 8 evaluated to True, it did not make a difference that 6 != 6 evaluates to False because the or operator was used. If we had used the and operator, this would evaluate to False.

In the third case, print(not(3 <= 1)), the not operator negates the False value that 3 <=1 returns.

Let’s substitute floats for integers and aim for False evaluations:

print((-0.2 > 1.4) and (0.8 < 3.1))	# One original expression is False
print((7.5 == 8.9) or (9.2 != 9.2))	# Both original expressions are False		
print(not(-5.7 <= 0.3))				# The original expression is True

In the example above,

  • and must have at least one False expression evaluate to False,
  • or must have both expressions evaluate to False,
  • not must have its inner expression be True for the new expression to evaluate to False.

If the results above seem unclear to you, we’ll go through some truth tables below to get you up to speed.

You can also write compound statements using and, or, and not:

not((-0.2 > 1.4) and ((0.8 < 3.1) or (0.1 == 0.1)))

Let’s look at the inner-most expression first: (0.8 < 3.1) or (0.1 == 0.1). This expression evaluates to True because both mathematical statements are True.

Now, we can take the returned value True and combine it with the next inner expression: (-0.2 > 1.4) and (True). This example returns False because the mathematical statement -0.2 > 1.4 is False, and (False) and (True) returns False.

Finally, we have the outer expression: not(False), which evaluates to True, so the final returned value if we print this statement out is:


The logical operators and, or, and not evaluate expressions and return Boolean values.

Truth Tables

There is a lot to learn about the logic branch of mathematics, but we can selectively learn some of it to improve our algorithmic thinking when programming.

Below are truth tables for the comparison operator ==, and each of the logic operators and, or, and not. While you may be able to reason them out, it can also be helpful to work to memorize them as that can make your programming decision-making process quicker.

== Truth Table

x == y Returns
True == True True
True == False False
False == True False
False == False True

AND Truth Table

x and y Returns
True and True True
True and False False
False and True False
False and False False

OR Truth Table

x or y Returns
True or True True
True or False True
False or True True
False or False False

NOT Truth Table

not x Returns
not True False
not False True

Truth tables are common mathematical tables used in logic, and are useful to memorize or keep in mind when constructing algorithms (instructions) in computer programming.

Using Boolean Operators for Flow Control

To control the stream and outcomes of a program in the form of flow control statements, we can use a condition followed by a clause.

A condition evaluates down to a Boolean value of True or False, presenting a point where a decision is made in the program. That is, a condition would tell us if something evaluates to True or False.

The clause is the block of code that follows the condition and dictates the outcome of the program. That is, it is the do this part of the construction “If x is True, then do this.”

The code block below shows an example of comparison operators working in tandem with conditional statements to control the flow of a Python program:

if grade >= 65:					# Condition
    print("Passing grade")		# Clause

    print("Failing grade")

This program will evaluate whether each student’s grade is passing or failing. In the case of a student with a grade of 83, the first statement will evaluate to True, and the print statement of Passing grade will be triggered. In the case of a student with a grade of 59, the first statement will evaluate to False, so the program will move on to execute the print statement tied to the else expression: Failing grade.

Because every single object in Python can be evaluated to True or False, the PEP 8 Style Guide recommends against comparing a value to True or False because it is less readable and will frequently return an unexpected Boolean. That is, you should avoid using if sammy == True: in your programs. Instead, compare sammy to another non-Boolean value that will return a Boolean.

Boolean operators present conditions that can be used to decide the eventual outcome of a program through flow control statements.


This tutorial discussed comparison and logical operators belonging to the Boolean type, as well as truth tables and using Booleans for program flow control.

You can learn more about other data types in our “Understanding Data Types” tutorial, and can read about conditional statements in our “How To Write Conditional Statements” tutorial.

We also have a free Python eBook, How To Code in Python that can support both beginners and those who need a quick reference.

Thanks for learning with the DigitalOcean Community. Check out our offerings for compute, storage, networking, and managed databases.

Learn more about us

Tutorial Series: How To Code in Python

Python is a flexible and versatile programming language that can be leveraged for many use cases, with strengths in scripting, automation, data analysis, machine learning, and back-end development. It is a great tool for both new learners and experienced developers alike.

About the authors

Still looking for an answer?

Ask a questionSearch for more help

Was this helpful?

Thank you so much for this! your a great teacher!!! I know that this was two years ago, but it has helped me today and helped me in my studying. I will continued going back to this when I need it!!!

    Try DigitalOcean for free

    Click below to sign up and get $200 of credit to try our products over 60 days!

    Sign up

    Join the Tech Talk
    Success! Thank you! Please check your email for further details.

    Please complete your information!

    Get our biweekly newsletter

    Sign up for Infrastructure as a Newsletter.

    Hollie's Hub for Good

    Working on improving health and education, reducing inequality, and spurring economic growth? We'd like to help.

    Become a contributor

    Get paid to write technical tutorials and select a tech-focused charity to receive a matching donation.

    Welcome to the developer cloud

    DigitalOcean makes it simple to launch in the cloud and scale up as you grow — whether you're running one virtual machine or ten thousand.

    Learn more
    DigitalOcean Cloud Control Panel