Introduction

In this chapter, we'll cover the basics of boolean values and operators in Python, including the AND, OR, and NOT operators, with examples from the field of mathematics.

Boolean Values

In Python, a boolean value is a data type that can have one of two values: True or False. These values are often used to represent the truth or falsehood of a condition or expression. For example, you might use a boolean value to indicate whether a number is prime or not, or whether a matrix is invertible or not.

Boolean Operators

Boolean values can be combined and manipulated using boolean operators. The three most common boolean operators in Python are AND, OR, and NOT.

The AND operator (and) returns True if both of its operands are True, and False otherwise. Here's a truth table for the AND operator:

The OR operator (or) returns True if at least one of its operands is True, and False otherwise. Here's a truth table for the OR operator:

The NOT operator (not) returns the opposite of its operand. If the operand is True, the NOT operator returns False, and vice versa. Here's a truth table for the NOT operator:

Examples

Here's an example of how to use boolean values and operators in Python, with a mathematics theme:

x = 5
y = 10

# Using the AND operator
print(x % 2 == 0 and y % 2 == 0)

Output:
False

# Using the OR operator
print(x % 2 == 0 or y % 2 == 0)

Output:
True

# Using the NOT operator
print(not x == y)

Output:
True

In this example, we use the AND, OR, and NOT operators to combine and manipulate boolean values. We use the and operator to check if both x and y are even, the or operator to check if either x or y is even, and the not operator to check if x is not equal to y.

Conclusion

In conclusion, boolean values and operators are fundamental concepts in programming with Python. With the ability to manipulate boolean values, you can create complex logical expressions and make decisions based on multiple conditions.