4.3: Boolean Operations

Learning Objectives

By the end of this section you should be able to

• Explain the purpose of logical operators.
• Describe the truth tables for and, or, and not.
• Create expressions with logical operators.
• Interpret if-else statements with conditions using logical operators.

Logical operator: and

Decisions are often based on multiple conditions. Ex: A program printing if a business is open may check that hour >= 9 and hour < 17. A logical operator takes condition operand(s) and produces True or False.

Python has three logical operators: and, or, and not. The and operator takes two condition operands and returns True if both conditions are true.

Table 4.1 Truth table: p and q.

p	q	p and q
True	True	True
True	False	False
False	True	False
False	False	False

Checkpoint: Example: Museum entry

Concepts in Practice \(\PageIndex{1}\): Using the and operator

Consider the example above. Jaden tries to enter when the capacity is 2500 and there are 2 hours before close. Can Jaden enter?

1. yes
2. no

Answer

a. 2500 < 3000 is True , and 2.5 > 1.0 is True , so Jaden can enter.

Concepts in Practice \(\PageIndex{2}\): Using the and operator

Consider the example above. Darcy tries to enter when the capacity is 3000. For what values of hrs_to_close will Darcy to be able to enter?

1. hrs_to close > 1.0
2. no such value

Answer

b. 3000 > 3000 is False . False and True is False . False and False is False . So no value of hrs_to_close will allow Darcy to enter.

Concepts in Practice \(\PageIndex{3}\): Using the and operator

Given is_admin = False and is_online = True, what is the value of is_admin and is_online?

1. True
2. False

Answer

b. False and True is False .

Concepts in Practice \(\PageIndex{4}\): Using the and operator

Given x = 8 and y = 21, what is the final value of z?

if (x < 10) and (y > 20):
  z = 5
else:
  z = 0

1. 0
2. 5

Answer

b. (8 < 10) and (21 > 20) evaluates to True and True, which is True . So the body of the if is executed, and z is assigned with 5 .

Logical operator: or

Sometimes a decision only requires one condition to be true. Ex: If a student is in the band or choir, they will perform in the spring concert. The or operator takes two condition operands and returns True if either condition is true.

Table 4.2: Truth table: p or q.

p	q	p or q
True	True	True
True	False	True
False	True	True
False	False	False

Checkpoint: Example: Streaming prompt

Concepts in Practice \(\PageIndex{5}\): Using the or operator

Given days = 21 and is_damaged is False, is the refund processed?

if (days < 30) or is_damaged:
  # Process refund

1. yes
2. no

Answer

a. (21 < 30) or False evaluates to True or False, which is True .

Concepts in Practice \(\PageIndex{6}\): Using the or operator

For what values of age is there no discount?

if (age < 12) or (age > 65):
  # Apply student/senior discount

1. age >= 12
2. age <= 65
3. (age >= 12) and (age <= 65)

Answer

c. The discount does not apply for ages between 12 and 65 inclusive.

Concepts in Practice \(\PageIndex{7}\): Using the or operator

Given a = 9 and b = 10, does the test pass?

if (a%2 == 0 and b%2 == 1) or (a%2 == 1 and b%2 == 0):
  # Test passed
else:
  # Test failed

1. yes
2. no

Answer

a. (9%2==0 and 10%2 ==1) evaluates to (False and False), which is False . (9%2 == 1 and 10%2 == 0) evaluates to (True and True), which is True . False or True is True . The if statement checks whether the numbers form an even-odd or odd-even pair.

Logical operator: not

If the computer is not on, press the power button. The not operator takes one condition operand and returns True when the operand is false and returns False when the operand is true.

not is a useful operator that can make a condition more readable and can be used to toggle a Boolean's value. Ex: is_on = not is_on.

Table 4.3 Truth table: not p.

p	not p
True	False
False	True

Checkpoint: Example: Diving warning

Concepts in Practice \(\PageIndex{8}\): Using the not operator

Given x = 13, what is the value of not(x < 10)?

1. True
2. False

Answer

a. not(13 < 10) evaluates to not(False), which is True .

Concepts in Practice \(\PageIndex{9}\): Using the not operator

Given x = 18, is x in the correct range?

if not(x > 15 and x < 20):
  # x in correct range

1. yes
2. no

Answer

b. not(18 > 15 and 18 < 20) evaluates to not(True and True), then not(True), and finally, False .

Concepts in Practice \(\PageIndex{10}\): Using the not operator

Given is_turn = False and timer = 65, what is the final value of is_turn?

if timer > 60:
  is_turn = not is_turn

1. True
2. False

Answer

a. 65 > 60 is True , so is_turn is assigned with not(False), which is True .

Try It: Speed limits

Write a program that reads in a car's speed as an integer and checks if the car's speed is within the freeway limits. A car's speed must be at least 45 mph but no greater than 70 mph on the freeway.

If the speed is within the limits, print "Good driving". Else, print "Follow the speed limits".

Interactive Code

Input

65

Answer

speed = int(input())

if (speed >= 45) and (speed <= 70):
print("Good driving")
else:
print("Follow the speed limits")