Logical operators

Table of Contents

Logical operators

Logical operators let you combine and invert conditions. They are used inside if, elif, and while statements to build more complex decisions.

Python has three main logical operators:

and
or
not

They work with expressions that are either True or False (Boolean values).

`and`: all conditions must be True

and combines two (or more) conditions and is True only if all parts are True.

General idea:

$$
A \text{ and } B \text{ is True only if both } A \text{ and } B \text{ are True.}
$$

In Python:

age = 20
has_ticket = True
if age >= 18 and has_ticket:
    print("You can enter.")
else:
    print("You cannot enter.")

Here:

age >= 18 is True
has_ticket is True
True and True is True, so "You can enter." is printed.

Truth table for and:

True and True → True
True and False → False
False and True → False
False and False → False

`or`: at least one condition must be True

or combines conditions and is True if at least one part is True.

General idea:

$$
A \text{ or } B \text{ is False only if both } A \text{ and } B \text{ are False.}
$$

Example:

is_admin = False
is_moderator = True
if is_admin or is_moderator:
    print("You have special access.")
else:
    print("Normal user access.")

Here:

is_admin is False
is_moderator is True
False or True is True, so "You have special access." is printed.

Truth table for or:

True or True → True
True or False → True
False or True → True
False or False → False

`not`: reverse a condition

not flips True to False and False to True.

General idea:

$$
\text{not } A \text{ is True if and only if } A \text{ is False.}
$$

Example:

logged_in = False
if not logged_in:
    print("Please log in first.")

logged_in is False
not logged_in is True
The message is printed.

Truth table for not:

not True → False
not False → True

Combining multiple logical operators

You can use and, or, and not together to build more detailed conditions.

Example:

age = 16
has_permission = True
if (age >= 18 or has_permission) and not (age < 10):
    print("Allowed.")
else:
    print("Not allowed.")

Read step by step:

age >= 18 → False
has_permission → True
age >= 18 or has_permission → False or True → True
age < 10 → False
not (age < 10) → not False → True
Final: True and True → True → "Allowed."

Operator precedence and parentheses

When you combine multiple logical operators, Python does not always evaluate them from left to right. There is an order (precedence):

not
and
or

For example:

result = True or False and False
print(result)

This is evaluated as:

False and False → False
True or False → True

So result is True.

If you want a different order, use parentheses:

result = (True or False) and False
print(result)  # This is False

Parentheses make your code clearer and safer, especially for beginners.

Common patterns with logical operators

Checking a range with `and`

A common use is to check that a value is between two numbers:

temperature = 22
if temperature >= 18 and temperature <= 25:
    print("Comfortable temperature.")

Python also allows this shorter form (just to recognize it when you see it):

if 18 <= temperature <= 25:
    print("Comfortable temperature.")

Multiple allowed values with `or`

Use or when any of several values is acceptable:

day = "Saturday"
if day == "Saturday" or day == "Sunday":
    print("It's the weekend!")

Typical beginner mistakes with logical operators

1. Using `and` instead of `or` (and vice versa)

Example:

color = "red"
# Wrong if you mean "red OR blue"
if color == "red" and color == "blue":
    print("Primary color.")

This condition is always False because color cannot be both "red" and "blue" at the same time.

Correct:

if color == "red" or color == "blue":
    print("Primary color.")

2. Forgetting to repeat the variable in comparisons

Incorrect:

age = 20
# This does NOT do what it seems
if age == 18 or 20:
    print("Age is 18 or 20")

age == 18 or 20 is interpreted as (age == 18) or 20, and 20 is always treated as True in this context, so the condition always passes.

Correct:

if age == 18 or age == 20:
    print("Age is 18 or 20")

3. Relying on precedence instead of using parentheses

This can make code confusing and lead to bugs:

age = 17
has_permission = True
with_parent = True
# Harder to read and can be misinterpreted
if age >= 18 or has_permission and with_parent:
    print("You can enter.")

Better with parentheses to show the intended logic:

if age >= 18 or (has_permission and with_parent):
    print("You can enter.")

Practice ideas

Try writing small if statements using logical operators:

Ask the user for their age and day of the week, and allow a discount if:

they are under 18 or
it is Wednesday.

Ask for a score, and print "Pass" only if it is at least 50 and not greater than 100.
Ask if it is raining and if the user has an umbrella; print whether they can go outside based on combinations of and, or, and not.

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Logical operators