CS9: Boolean Operations
Master NOT, AND, OR truth tables, combining Boolean operators in conditions, De Morgan's Laws, and operator precedence.
📋 What are Boolean Operations?
Boolean operations work on Boolean values (TRUE and FALSE) to produce a Boolean result. They are used to combine or invert conditions in IF statements and WHILE loops.
The three Boolean operators are:
- NOT - inverts (reverses) a Boolean value
- AND - returns TRUE only if BOTH operands are TRUE
- OR - returns TRUE if at least ONE operand is TRUE
🔄 NOT
NOT reverses a Boolean value. NOT TRUE = FALSE, NOT FALSE = TRUE. It is used to invert a condition.
| A | NOT A |
|---|---|
| TRUE | FALSE |
| FALSE | TRUE |
NOT in Pseudo-code
isRaining ← TRUE
IF NOT isRaining THEN
OUTPUT "Let's go outside!"
ELSE
OUTPUT "Stay inside"
ENDIF
// Output: "Stay inside" (because NOT TRUE = FALSE)
🔗 AND
AND returns TRUE only when BOTH conditions are TRUE. If either one is FALSE, the result is FALSE.
| A | B | A AND B |
|---|---|---|
| TRUE | TRUE | TRUE |
| TRUE | FALSE | FALSE |
| FALSE | TRUE | FALSE |
| FALSE | FALSE | FALSE |
AND in Pseudo-code
IF age >= 18 AND hasID = TRUE THEN
OUTPUT "You can buy alcohol"
ELSE
OUTPUT "You cannot buy alcohol"
ENDIF
// Both conditions must be TRUE to allow the purchase
AND Rule:
Think of AND as a strict gatekeeper.
TRUE AND TRUE = TRUE (both pass)
Anything else = FALSE (at least one fails)
Think of AND as a strict gatekeeper.
TRUE AND TRUE = TRUE (both pass)
Anything else = FALSE (at least one fails)
🔀 OR
OR returns TRUE when at least ONE condition is TRUE. Only returns FALSE when BOTH conditions are FALSE.
| A | B | A OR B |
|---|---|---|
| TRUE | TRUE | TRUE |
| TRUE | FALSE | TRUE |
| FALSE | TRUE | TRUE |
| FALSE | FALSE | FALSE |
OR in Pseudo-code
IF day = "Saturday" OR day = "Sunday" THEN
OUTPUT "It's the weekend!"
ELSE
OUTPUT "It's a weekday"
ENDIF
// Only one condition needs to be TRUE
OR Rule:
Think of OR as a lenient gatekeeper.
FALSE OR FALSE = FALSE (both fail)
Anything else = TRUE (at least one passes)
Think of OR as a lenient gatekeeper.
FALSE OR FALSE = FALSE (both fail)
Anything else = TRUE (at least one passes)
🧮 Combining Boolean Operators
You can combine multiple Boolean operators in a single condition. Use brackets to make the order of evaluation clear.
Combining AND and OR
IF (age >= 18 AND hasID = TRUE) OR isMember = TRUE THEN
OUTPUT "Access granted"
ENDIF
Access is granted if: (over 18 AND has ID) OR is a member.
Complex Condition
IF (score >= 70 OR coursework >= 80) AND attendance >= 90 THEN
OUTPUT "Pass with merit"
ENDIF
Pass with merit requires: (high score OR high coursework) AND good attendance.
Brackets matter! The condition "A AND B OR C" is ambiguous. It could mean "(A AND B) OR C" or "A AND (B OR C)" which give different results. Always use brackets to make your intention clear.
Brackets Change the Result
Let A = FALSE, B = FALSE, C = TRUE
(A AND B) OR C = (FALSE AND FALSE) OR TRUE = FALSE OR TRUE = TRUE
A AND (B OR C) = FALSE AND (FALSE OR TRUE) = FALSE AND TRUE = FALSE
Same values, different result - brackets matter!
📐 De Morgan's Laws
De Morgan's Laws allow you to simplify complex Boolean expressions by "distributing" NOT over AND/OR. They state that the opposite of an AND expression is an OR expression of the opposites, and vice versa.
De Morgan's Laws:
NOT (A AND B) = (NOT A) OR (NOT B)
NOT (A OR B) = (NOT A) AND (NOT B)
When you push NOT through AND, it becomes OR (and vice versa).
Each individual condition is also negated.
NOT (A AND B) = (NOT A) OR (NOT B)
NOT (A OR B) = (NOT A) AND (NOT B)
When you push NOT through AND, it becomes OR (and vice versa).
Each individual condition is also negated.
De Morgan's Law Example 1
Original: NOT (age >= 18 AND hasID = TRUE)
This means: it is NOT the case that both age >= 18 AND has ID.
Applying De Morgan's: (age < 18) OR (hasID = FALSE)
This means: either too young OR no ID - same meaning, simpler expression!
De Morgan's Law Example 2
Original: NOT (raining = TRUE OR snowing = TRUE)
This means: it is NOT the case that it is raining OR snowing.
Applying De Morgan's: (raining = FALSE) AND (snowing = FALSE)
This means: it is not raining AND it is not snowing - same meaning!
| Original Expression | De Morgan Equivalent | English Meaning |
|---|---|---|
| NOT (x > 0 AND x < 100) | x <= 0 OR x >= 100 | x is outside the range 0-100 |
| NOT (a = TRUE OR b = TRUE) | a = FALSE AND b = FALSE | Both a and b are false |
| NOT (age >= 18 AND hasPassport) | age < 18 OR NOT hasPassport | Either too young or no passport |
📊 Operator Precedence
Boolean operators have an order of precedence: NOT is evaluated first, then AND, then OR. Use brackets to override this order.
Full Precedence (highest to lowest):
1. Brackets ()
2. NOT
3. AND
4. OR
So "NOT A OR B AND C" means "(NOT A) OR (B AND C)"
1. Brackets ()
2. NOT
3. AND
4. OR
So "NOT A OR B AND C" means "(NOT A) OR (B AND C)"
Precedence Example
NOT TRUE OR TRUE AND FALSE
Step 1: NOT TRUE = FALSE
Step 2: TRUE AND FALSE = FALSE
Step 3: FALSE OR FALSE = FALSE
⚠️ Common Mistakes
| Mistake | Why It's Wrong | How to Fix It |
|---|---|---|
| Using AND when you mean OR | "age < 13 AND age > 19" is always FALSE | Use OR: "age < 13 OR age > 19" |
| Forgetting brackets with mixed operators | A AND B OR C is ambiguous | Write (A AND B) OR C explicitly |
| NOT (A AND B) = NOT A AND NOT B | This is WRONG - De Morgan says OR, not AND | NOT (A AND B) = NOT A OR NOT B |
| Double negation confusion | NOT NOT TRUE = TRUE, but it's confusing | Simplify: remove double NOTs |
❓ Practice Questions
Q1: Complete the truth table for A AND B where A = TRUE, B = FALSE.
Q2: Evaluate: NOT (TRUE OR FALSE)
Q3: Use De Morgan's Laws to simplify: NOT (x >= 0 AND x <= 100)
Q4: Write a condition that checks if a person is eligible for a student discount (age < 18 OR hasStudentCard = TRUE) AND isShopping = TRUE.
Q5: Evaluate step by step: NOT FALSE AND TRUE OR FALSE
✅ Answers
- TRUE AND FALSE = FALSE. Both must be TRUE for AND to return TRUE.
- TRUE OR FALSE = TRUE. Then NOT TRUE = FALSE.
- Using De Morgan's: NOT(x >= 0) OR NOT(x <= 100) = x < 0 OR x > 100.
-
IF (age < 18 OR hasStudentCard = TRUE) AND isShopping = TRUE THEN OUTPUT "Student discount applied" ENDIF - Step 1: NOT FALSE = TRUE (NOT has highest precedence). Step 2: TRUE AND TRUE = TRUE (AND next). Step 3: TRUE OR FALSE = TRUE (OR lowest). Result: TRUE.
🎯 Exam Tips
- Memorise the truth tables for NOT, AND, and OR
- AND needs BOTH to be TRUE; OR needs at least ONE
- Use brackets whenever combining AND and OR in the same condition
- De Morgan's: NOT(AND) becomes OR of NOTs, NOT(OR) becomes AND of NOTs
- Precedence: NOT first, then AND, then OR
- When simplifying conditions, apply De Morgan's Laws to make code clearer
⚠️ Common Errors
✗ Thinking AND and OR are interchangeable ✓ AND requires ALL conditions to be true; OR requires at least ONE condition to be true. They produce different results and are not interchangeable.
✗ Forgetting that NOT reverses a Boolean value ✓ NOT TRUE = FALSE and NOT FALSE = TRUE. NOT flips the result — it is used to negate conditions, e.g. WHILE NOT finished.
✗ Assuming AND is evaluated before OR without brackets ✓ AND has higher precedence than OR in most languages. Use brackets to make intent clear: (A OR B) AND C is different from A OR (B AND C).
✗ Confusing NOT with negative numbers or minus signs ✓ NOT is a logical operator that reverses True/False. It is not the same as the arithmetic minus sign. NOT(5 > 3) = FALSE, not -5.
✍️ Model Answer
Full-Mark Response
A login system requires a username of at least 5 characters AND a password of at least 8 characters. The user is locked out after 3 failed attempts. Write pseudo-code using Boolean operators to implement this. [5 marks]
attempts ← 0 loggedin ← FALSE WHILE attempts < 3 AND loggedin = FALSE INPUT 'Username: ', username INPUT 'Password: ', password IF LENGTH(username) >= 5 AND LENGTH(password) >= 8 THEN OUTPUT 'Login successful' loggedin ← TRUE ELSE attempts ← attempts + 1 IF NOT loggedin AND attempts < 3 THEN OUTPUT 'Invalid credentials, try again' ENDIF ENDIF ENDWHILE IF NOT loggedin THEN OUTPUT 'Account locked: too many attempts' ENDIF
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Computational Thinking — 40%): Demonstrate knowledge and understanding of the principles and concepts of computer science, including Boolean operations: AND, OR and NOT for AQA 8525, OCR J277 & Edexcel 1CP2.
AO2 (Application — 40%): Apply knowledge and understanding of computer science, including Boolean operations: AND, OR and NOT to analyse problems in computational terms and to design, write and evaluate solutions.
AO3 (Evaluation — 20%): Evaluate the effectiveness, correctness and efficiency of computational solutions, including Boolean operations: AND, OR and NOT, and make reasoned judgements about trade-offs.
📝 Exam Technique
GCSE Computer Science Exam Tips:
AND needs ALL conditions True, OR needs ANY condition True, NOT reverses. Use brackets to make complex conditions clear. Build truth tables if asked to evaluate Boolean expressions. For validation, AND is used when ALL criteria must be met; OR when ANY criterion is sufficient. Remember AND has higher precedence than OR — use brackets to override.
AND needs ALL conditions True, OR needs ANY condition True, NOT reverses. Use brackets to make complex conditions clear. Build truth tables if asked to evaluate Boolean expressions. For validation, AND is used when ALL criteria must be met; OR when ANY criterion is sufficient. Remember AND has higher precedence than OR — use brackets to override.
📝 Exam Questions by Topic
🎬 Video Resources
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