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

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• Logical operators combine or modify Boolean expressions (and, or, not)
  • Create more complex conditions in programming by evaluating multiple expressions

• and

  operator returns

  [True](https://www.fiveableKeyTerm:TRUE)

  if both operands are

  True

  , otherwise returns

  [False](https://www.fiveableKeyTerm: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")