4.3 Boolean operations

Boolean operations and logic are fundamental to programming, allowing us to create complex conditions and control program flow. By combining logical operators like 'and', 'or', and 'not', we can evaluate multiple expressions and make decisions based on their outcomes.

These concepts are crucial for writing efficient and flexible code. Understanding truth tables and Boolean algebra helps us analyze and simplify logical expressions, leading to clearer and more maintainable programs.

Boolean Operations and Logic

Logical operators and complex conditions

• Logical operators combine or modify Boolean expressions (and, or, not)
  • Create more complex conditions in programming by evaluating multiple expressions
• and operator returns True if both operands are True, otherwise returns False (logical conjunction)
  • Example: (x > 0) and (x < 10) is True if x is between 0 and 10 (exclusive)
• or operator returns True if at least one operand is True, otherwise returns False (logical disjunction)
  • Example: (x < 0) or (x > 10) is True if x is less than 0 or greater than 10
• not operator returns the opposite Boolean value of the operand (logical negation)
  • Example: not (x > 0) is True if x is less than or equal to 0
• Logical operators enable the construction of compound conditions that depend on multiple Boolean expressions

Expressions with and, or, not

• and operator syntax: expression1 and expression2
  • Evaluates to True only if both expression1 and expression2 are True
  • Example: (age >= 18) and (age <= 65) checks if age is between 18 and 65 (inclusive)
• or operator syntax: expression1 or expression2
  • Evaluates to True if at least one of expression1 or expression2 is True
  • Example: (score < 60) or (absences > 5) checks if score is below 60 or absences exceed 5
• not operator syntax: not expression
  • Negates the Boolean value of the expression
  • Example: not (is_weekend) is True if is_weekend is False

Boolean logic in if-else statements

• if-else statements execute code conditionally based on Boolean expressions
  • if block runs if the condition is True, else block runs if the condition is False
• Syntax:

  if condition:
      # Code to execute if condition is True
  else:
      # Code to execute if condition is False
  

• Boolean expressions with logical operators can be used as conditions in if-else statements
  • Example:

    if (temperature > 30) and (humidity > 60):
        print("It's hot and humid")
    else:
        print("The weather is pleasant")
    

Truth tables for Boolean expressions

• Truth tables visualize all possible combinations of input values and their corresponding output values (truth values)

  • Each row represents a unique combination of input values
  • The output column shows the result of the Boolean expression for each combination

• Truth table for the and operator:

  A	B	A and B
  True	True	True
  True	False	False
  False	True	False
  False	False	False

• Truth table for the or operator:

  A	B	A or B
  True	True	True
  True	False	True
  False	True	True
  False	False	False

• Truth table for the not operator:

  A	not A
  True	False
  False	True

• Compound Boolean expressions can be analyzed using truth tables

  • Evaluate each subexpression and combine the results according to the logical operators used
  • Example: (A and B) or (not C)

Boolean Algebra

• Boolean algebra is a mathematical system for reasoning about logical expressions
• It provides rules and laws for manipulating Boolean expressions:
  • Commutative laws: A and B = B and A, A or B = B or A
  • Associative laws: (A and B) and C = A and (B and C), (A or B) or C = A or (B or C)
  • Distributive laws: A and (B or C) = (A and B) or (A and C), A or (B and C) = (A or B) and (A or C)
• These laws are fundamental to simplifying and analyzing complex Boolean expressions in programming

Conditional Statements and Program Flow

Boolean logic in if-else statements

• if-elif-else statements check multiple conditions in sequence
  • elif (short for "else if") blocks run if the preceding if or elif conditions are False
  • Only the first if or elif block with a True condition is executed
• Syntax:

  if condition1:
      # Code to execute if condition1 is True
  elif condition2:
      # Code to execute if condition1 is False and condition2 is True
  else:
      # Code to execute if all preceding conditions are False
  

• Nested if-else statements create more complex decision-making structures
  • if-else statements can be placed inside other if, elif, or else blocks
  • Allows for hierarchical conditions and fine-grained control over program flow
  • Example:

    if age >= 18:
        if has_license:
            print("You can drive")
        else:
            print("You need a license to drive")
    else:
        print("You are too young to drive")