Decision Structures and Boolean Logic Notes

Relational Operators and Expressions

• Relational operators compare two values (numbers or strings) to determine their relative order:
  • > : Greater than
  • < : Less than
  • >= : Greater than or equal to
  • <= : Less than or equal to
  • == : Equal to
  • != : Not equal to
• Relational expressions evaluate to Boolean values: True or False.
• Equality comparison (==) must not be confused with variable assignment (=).

The if Statement

• An if statement is a control structure that enables conditional execution of statements (one-way decision).
• Syntax requirements: A colon : follows the Boolean condition, and the controlled body of statements must be indented.
• Python truthiness rules: Numeric value 0 evaluates to False, whereas any non-zero numeric value evaluates to True.
• Turtle graphics state methods like turtle.isdown() and turtle.isvisible() return Boolean values usable in if conditions.

The if-else Statement and Conditional Expressions

• An if/else statement provides a dual-alternative structure executing one block if the condition is True and an alternate block if False.
• The if clause and else clause must be vertically aligned at the same indentation level.
• Conditional expression (ternary operator) syntax: x if condition else y. Evaluates condition; returns x if True, otherwise returns y.

String Comparison

• Strings are compared character-by-character based on their ASCII character values.
• String comparisons are case-sensitive.
• If a shorter string is a proper prefix/substring of a longer string, the longer string is evaluated as greater.

Nested if and if-elif-else Decision Structures

• Nested if statements place decision structures inside the body of an existing if or else block.
• The if/elif/else statement provides a multi-way decision chain that tests conditions sequentially until one evaluates to True.
• A trailing else clause serves as a default fallback to handle remaining cases or catch invalid user inputs.

Logical Operators and Precedence

• Logical operators combine relational expressions into compound Boolean expressions:
  • and : Returns True if both sub-expressions are True.
  • or : Returns True if either sub-expression is True.
  • not : Reverses the truth value of an expression.
• Logical operator precedence order: not (highest) > and > or (lowest).
• Overall operator precedence: Arithmetic operators > Relational operators > Logical operators.
• Short-circuit evaluation stops evaluating compound expressions as soon as the outcome is guaranteed:
  • For or: If the left operand is True, the right operand is skipped.
  • For and: If the left operand is False, the right operand is skipped.

Numeric Ranges, Input Validation, and Flags

• Ranges can be checked using logical operators (e.g., grade >= 0 and grade <= 100) or chained relational operators (e.g., 0 <= grade <= 100).
• Input validation inspects user data prior to processing to prevent invalid inputs or division-by-zero errors.
• Boolean variables belong to the bool data type and store either True or False.
• A flag is a Boolean variable used to signal the presence or absence of a specific condition in a program.

Questions & Discussion

• Three-Grade Average Task:
  • Prompt user for 3 test grades.
  • Compute sum and average: $\text{average} = \frac{\text{grade}_1 + \text{grade}_2 + \text{grade}_3}{3}$.
  • If $\text{average} > 60$, display "Pass"; otherwise display "Fail".
• Character Inequality Check:
  • Expression evaluating to True if str c is not equal to a single space: c != ' '.
• Conditional Bonus Calculation:
  • Expression assigning $10000$ to bonus if goods_sold > 500000, else $0$: bonus = 10000 if goods_sold > 500000 else 0.
• Finding Minimum Value:
  • Code logic to assign the smallest of integer variables x, y, and z to variable min.

Here are practice quiz questions based on your material:

Practice Quiz

1. Relational Expressions: Given $x = 10$ and $y = 7$, evaluate the Boolean truth value of each expression:

   • $x == 10$
   • $x < y + 1$
   • $x != y$

2. Truthiness in Python: In Python conditional statements, what Boolean value does the integer $0$ evaluate to, and what do non-zero numeric values evaluate to?

3. Operator Precedence: Rank the following operator categories from highest precedence to lowest precedence:

   • Logical operators (not, and, or)
   • Arithmetic operators (+, -, *, /)
   • Relational operators (>, <, ==, !=)

4. Short-Circuit Evaluation:

   • Under what condition does the or operator stop evaluating the second operand?
   • Under what condition does the and operator stop evaluating the second operand?

5. Conditional Expressions: Write a single-line conditional expression that assigns $10000$ to bonus if goods_sold > 500000, and otherwise assigns $0$.

6. String Comparison: How does Python compare strings when using relational operators such as < or >?