Logical Operators Part 4

Part of the Fundamentals section of Coddy's Python journey — lesson 19 of 77.

When working with logical expressions, sometimes we need to simplify or rearrange them. This is particularly useful when dealing with complex conditions that combine multiple and and or operators.

De Morgan's Laws provide rules for transforming logical expressions. These transformations help make code more readable and easier to understand.

First Law: not (A and B) is the same as (not A) or (not B)

Notice two things happen when you distribute not into the expression: each operand gets negated (A becomes not A, B becomes not B), and the operator flips — and becomes or. The not doesn't just negate the values; it also switches the connecting operator between them.

For example:

# Let's check if a number is NOT (between 1 and 10)
number = 15

# These two expressions are equivalent:
result1 = not (number >= 1 and number <= 10)
result2 = (not number >= 1) or (not number <= 10)

print(result1)  # True
print(result2)  # True

Second Law: not (A or B) is the same as (not A) and (not B)

The same two-step rule applies here: each operand gets negated, and the operator flips — this time or becomes and. Think of it as: distributing not always flips and ↔ or while negating each part.

For example:

# Checking if a person is NOT (a student or employed)
is_student = False
is_employed = False

# These two expressions are equivalent:
result1 = not (is_student or is_employed)
result2 = (not is_student) and (not is_employed)

print(result1)  # True
print(result2)  # True

Complex Example with Both AND and OR: Sometimes you need conditions that combine both operators. Here's a practical example:

# Checking if we CAN'T accept a job application
# We reject if: (no experience AND no degree) OR doesn't meet age requirement

has_experience = False
has_degree = False
meets_age = True

# Complex condition using both AND and OR
reject_application = (not has_experience and not has_degree) or not meets_age

print(reject_application)  # True (rejected because no experience AND no degree)

# This can also be written using De Morgan's Laws:
# accept = (experience OR degree) AND meets age; reject = not accept
accept_application = (has_experience or has_degree) and meets_age
reject_application2 = not accept_application

print(reject_application2)  # True (same result, different logic)

When to use De Morgan's Laws:

To make negative conditions easier to read
To simplify complex logical expressions
To convert between different representations of the same logic

Challenge

Beginner

You're helping a pet shop create a system to determine if they can sell a pet to a customer.

Initialize the following variables:

has_license with the value True
has_space with the value True
has_experience with the value False

Write logical expressions to determine if:

can_sell_regular_pet: Customer can buy a regular pet if they have EITHER a license OR experience, AND they must have space
can_sell_exotic_pet: Customer can buy an exotic pet if they have BOTH a license AND experience, AND they must have space
cannot_sell_any_pet: The shop CANNOT sell any pet if the customer has NO license AND NO experience, OR they have NO space

Expected Results with the given values:

can_sell_regular_pet: True (has license and space)
can_sell_exotic_pet: False (no experience)
cannot_sell_any_pet: False (has both license and space)

Cheat sheet

De Morgan's Laws — rules for transforming logical expressions:

not (A and B) → (not A) or (not B)
not (A or B) → (not A) and (not B)

When distributing not: each operand gets negated and the operator flips (and ↔ or).

# First Law example
result = not (number >= 1 and number <= 10)
result = (not number >= 1) or (not number <= 10)  # equivalent

# Second Law example
result = not (is_student or is_employed)
result = (not is_student) and (not is_employed)  # equivalent

Try it yourself

# Initialize variables

# Calculate conditions
can_sell_regular_pet = 
can_sell_exotic_pet = 
cannot_sell_any_pet =

# Don't delete the lines below
print("Can sell regular pet:", can_sell_regular_pet)
print("Can sell exotic pet:", can_sell_exotic_pet)
print("Cannot sell any pet:", cannot_sell_any_pet)