Operators & Expressions

Why read this? An expression is how you compute new values from existing ones. Every calculator, every formula, every decision your program makes involves operators. Mastering operators is like learning the verbs of the Python language — they're how you make things happen.

🎯 Learning Objectives

1. Use all arithmetic, comparison, logical, and membership operators
2. Predict expression evaluation using precedence and associativity rules
3. Distinguish between == (value equality) and is (identity)
4. Write boolean expressions with and, or, not
5. Use in to check membership in collections

📋 Prerequisites

• Variables & Data Types — You need to understand variables and types.
• Input, Output & Formatted Strings — Useful but not essential.

📖 Core Content

4.1 What Is an Expression?

pseudo
Expression → Python evaluates it → Value
   2 + 3              →              5
  "A" + "B"           →             "AB"
   len("hi")          →              2

4.2 Arithmetic Operators — Review and Extend

python
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# runnable
print(7 // 3)    # 2    (2*3=6, remainder 1)
print(-7 // 3)   # -3   (-3*3=-9, remainder 2) ← NOT -2!
print(7 // -3)   # -3
print(-7 // -3)  # 2

pseudo
2
-3
-3
2

4.3 Comparison Operators — Making Decisions

python
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# runnable
a = 10
b = 5
print(a == b)    # False  (equal to)
print(a != b)    # True   (not equal to)
print(a > b)     # True   (greater than)
print(a < b)     # False  (less than)
print(a >= b)    # True   (greater than or equal)
print(a <= b)    # False  (less than or equal)

pseudo
False
True
True
False
True
False

⚠️ Critical: = is ASSIGNMENT (store a value). == is COMPARISON (check if equal). This is the #1 mistake beginners make!

4.4 Chained Comparisons

python
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# runnable
x = 15
print(10 < x < 20)    # True (10 < 15 and 15 < 20)
print(10 < x < 12)    # False (15 is not < 12)
# Equivalent to:
print(10 < x and x < 20)  # True

pseudo
True
False
True

4.5 Logical Operators — and, or, not

python
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# runnable
age = 22
has_license = True
# and: both must be True
print(age >= 18 and has_license)   # True (both conditions are True)
# or: at least one must be True
has_car = False
print(has_license or has_car)      # True (has_license is True)
# not: reverses the boolean
is_weekend = False
print(not is_weekend)              # True

pseudo
True
True
True

4.6 Short-Circuit Evaluation

python
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# runnable
def get_true():
    print("get_true called")
    return True
def get_false():
    print("get_false called")
    return False
# Short-circuit with and: if first is False, second is NOT evaluated
print(get_false() and get_true())  # get_true is NEVER called!
print("---")
# Short-circuit with or: if first is True, second is NOT evaluated
print(get_true() or get_false())   # get_false is NEVER called!

pseudo
get_false called
False
---
get_true called
True

4.7 Membership Operators — in and not in

python
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# runnable
word = "python"
print("p" in word)       # True
print("z" in word)       # False
print("tho" in word)     # True (substring exists)
print("xyz" not in word) # True (xyz is NOT in word)
# Works with lists too
fruits = ["apple", "banana", "cherry"]
print("banana" in fruits)    # True
print("grape" in fruits)     # False

pseudo
True
False
True
True
True
False

4.8 Identity Operators — is and is not

python
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# runnable
a = [1, 2, 3]
b = [1, 2, 3]    # b has the same values as a
c = a             # c points to the SAME list as a
print(a == b)     # True  (values are equal)
print(a is b)     # False (different objects in memory)
print(a is c)     # True  (same object)
# For simple types like small integers, Python sometimes reuses objects
x = 5
y = 5
print(x is y)     # True (Python caches small integers)

pseudo
True
False
True
True

⚠️ Rule of thumb: Use == for comparing values. Use is for checking None (if x is None:). Never use is to compare numbers or strings in normal code — it behaves unpredictably across implementations.

4.9 Operator Precedence — The Complete Table

• Left-to-right: Most operators (+, -, *, /, //, %, and, or, etc.)
• Right-to-left: ** (exponentiation) and assignment operators

4.10 Worked Example 1: Complex Expression Evaluation

python
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# runnable
result = 5 + 3 * 2 ** 2 // 4 - 1
print(result)

1. 2 ** 2 → 4 (exponent: highest of the actual operators)
2. 3 * 4 // 4 → 12 // 4 → 3 (* and // same precedence, left to right)
3. 5 + 3 - 1 → 7 Output: 7

4.11 Worked Example 2: Logical Expression with Comparisons

python
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# runnable
x = 10
y = 20
z = 15
result = x < y and y > z or not x == z
print(result)

1. x < y → 10 < 20 → True
2. y > z → 20 > 15 → True
3. x == z → 10 == 15 → False
4. not False → True
5. True and True → True
6. True or True → True Output: True

4.12 Worked Example 3: Leap Year Condition

python
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# runnable
year = 2024
is_leap = (year % 400 == 0) or (year % 4 == 0 and year % 100 != 0)
print(f"{year} is a leap year? {is_leap}")
year = 1900
is_leap = (year % 400 == 0) or (year % 4 == 0 and year % 100 != 0)
print(f"{year} is a leap year? {is_leap}")
year = 2000
is_leap = (year % 400 == 0) or (year % 4 == 0 and year % 100 != 0)
print(f"{year} is a leap year? {is_leap}")

pseudo
2024 is a leap year? True
1900 is a leap year? False
2000 is a leap year? True

4.13 Worked Example 4: Safe Division with Short-Circuit

python
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# runnable
def divide_safe(a, b):
    # Short-circuit: if b == 0, the division never happens
    return b != 0 and a / b
print(divide_safe(10, 2))    # 5.0
print(divide_safe(10, 0))    # False (b != 0 is False, so a/b never runs)

pseudo
5.0
False

Note: In real code, you'd use if/else for safety. This example demonstrates short-circuit behavior.

4.14 Worked Example 5: Combining All Operator Types

python
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# runnable
age = 25
salary = 50000
has_job = True
credit_score = 720
# Loan eligibility: age >= 21, salary > 30000, has job, good credit
eligible = age >= 21 and salary > 30000 and has_job and credit_score >= 650
print(f"Loan eligible: {eligible}")
# Also check if they're in a "premium" category
premium = salary > 100000 or (salary > 50000 and credit_score > 750)
print(f"Premium customer: {premium}")
# Not a risky candidate
risky = not has_job or credit_score < 600
print(f"Risky: {risky}")

pseudo
Loan eligible: True
Premium customer: False
Risky: False

📐 Key Concepts Reference

⚠️ Common Pitfalls

Pitfall 1: Confusing = with ==

Pitfall 2: and/or Return Values (Not Boolean)

python
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print(0 and 5)    # 0 (falsy value returned)
print(3 and 5)    # 5 (last truthy value)
print(0 or 5)     # 5 (first truthy value)
print(3 or 5)     # 3 (first truthy value)

Pitfall 3: Floating-Point Equality

python
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print(0.1 + 0.2)  # 0.30000000000000004
print(0.1 + 0.2 == 0.3)  # False

Pitfall 4: is for Value Comparison

📝 Practice Questions

Q1: Evaluate step-by-step: 10 + 2 * 3 ** 2 - 6 // 4

Answer:

pseudo
10 + 2 * 3 ** 2 - 6 // 4
= 10 + 2 * 9 - 6 // 4    (exponent: 3**2 = 9)
= 10 + 18 - 6 // 4        (multiply: 2*9 = 18)
= 10 + 18 - 1             (floor division: 6//4 = 1)
= 27

Q2: What's the output?

python
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print(5 > 3 and 2 < 4 or not 7 == 7)

Answer:

pseudo
True

Step-by-step:

1. 5 > 3 → True
2. 2 < 4 → True
3. True and True → True
4. 7 == 7 → True
5. not True → False
6. True or False → True Q3: What's the difference between print(10 / 3) and print(10 // 3)?

Answer:

• 10 / 3 → 3.3333333333333335 (float division, precise)
• 10 // 3 → 3 (floor division, rounds down)

/ always returns float. // returns int when both operands are int (but float if either is float). Q4: What does this code output and why?

python
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print("a" in "apple")
print("app" in "apple")
print("x" not in "apple")

Answer:

pseudo
True
True
True

• "a" is a character in "apple" → True
• "app" is a substring of "apple" → True
• "x" is NOT in "apple" → not in returns True Q5: Fix the error in this code:

python
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x = input("Number: ")
if x % 2 == 0:
    print("Even")

Answer: Error: TypeError: not all arguments converted during string formatting or similar. Fix: Convert input to int: x = int(input("Number: ")) input() returns a string. The % operator on strings does something different (formatting). Q6: What does -7 // 3 evaluate to? Why?

Answer: -7 // 3 → -3

Because floor division rounds DOWN to negative infinity. -7/3 = -2.333.... Rounding down gives -3 (more negative). Not -2 (which would be rounding toward zero). Q7: Write a condition that checks if a number n is between 1 and 100 (inclusive).

Answer:

python
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# runnable
n = 50
if 1 <= n <= 100:
    print(f"{n} is between 1 and 100")

Or: if n >= 1 and n <= 100: Q8: What does this output?

python
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print(False or True and False)

Answer:

pseudo
False

• True and False → False (and has higher precedence than or)
• False or False → False Q9: Write a program that checks if a character entered by the user is a vowel.

Answer:

python
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# runnable
ch = input("Enter a letter: ").lower()
is_vowel = ch in "aeiou"
print(f"Is '{ch}' a vowel? {is_vowel}")

Q10: What's the value of this expression?

python
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(15 % 4) == 3 and (2 ** 3) > 10 or "py" in "python"

Answer:

pseudo
True

Step-by-step:

1. 15 % 4 → 3
2. 3 == 3 → True
3. 2 ** 3 → 8
4. 8 > 10 → False
5. True and False → False
6. "py" in "python" → True
7. False or True → True

🔗 Cross-References

• Next Topic: Strings — Basics & Operations
• Previous Topic: Input, Output & Formatted Strings
• BSCS1001 Computational Thinking: Boolean logic (and/or/not) is the foundation of decision-making in algorithms.
• BSCS2002 PDSA: Bitwise operators (&, |, <<, >>) become important for low-level data structures.
• Reference: Python for Everybody, Chapter 2 (Sections 2.5-2.8)
• Video: L9: Operators & expressions part 1, L10: Operators & expressions part 2 Join Discord Previous3. Input & OutputNext5. Strings Basics