1.3.1 Truth tables
Logical Operators and Truth Tables
A truth table shows every possible combination of Boolean (True/False) inputs for a logical expression and the corresponding output. They are used to analyse the behaviour of conditions in programs and to solve logic problems.
The three logical operators are AND, OR and NOT. In Python (PLS): and, or, not.
Single-Operator Truth Tables
AND returns True only when both inputs are True.
| A | B | A AND B |
|---|---|---|
| False | False | False |
| False | True | False |
| True | False | False |
| True | True | True |
Only one row gives True. Memory aid: AND is strict — all inputs must be True.
OR returns True when at least one input is True.
| A | B | A OR B |
|---|---|---|
| False | False | False |
| False | True | True |
| True | False | True |
| True | True | True |
Only one row gives False (both False). Memory aid: OR is generous — any True input gives True.
NOT has only one input and simply inverts it.
| A | NOT A |
|---|---|
| False | True |
| True | False |
Three-Input Truth Tables
With three inputs (A, B, C), there are 2³ = 8 possible combinations. The table is built by systematically listing all combinations — A alternates every 4 rows, B every 2 rows, C every row.
Worked example: (A AND B) OR C
| A | B | C | A AND B | (A AND B) OR C |
|---|---|---|---|---|
| F | F | F | F | F |
| F | F | T | F | T |
| F | T | F | F | F |
| F | T | T | F | T |
| T | F | F | F | F |
| T | F | T | F | T |
| T | T | F | T | T |
| T | T | T | T | T |
The expression is True in 5 of 8 cases. It is only False when C is False and A AND B is also False.
Applying Truth Tables to Problems
Truth tables can model real access control or decision logic. Example: a door unlocks if a PIN is correct AND a valid card is present, OR a master override is active.
pin_correct = True
card_valid = False
override = True
# (pin_correct AND card_valid) OR override
if (pin_correct and card_valid) or override:
print("Door unlocked")
else:
print("Access denied")
# Output: Door unlocked (because override is True)Key Takeaways
- AND: True only when both inputs are True.
- OR: True when at least one input is True.
- NOT: inverts its single input.
- Two inputs → 4 rows (2²); three inputs → 8 rows (2³).
- Build complex expressions by evaluating sub-expressions as intermediate columns.