Truth tables
Key Notes:
What is a Truth Table?
- A truth table is a chart used to show all possible truth values of a logical expression.
- It helps in understanding how logical operators (AND, OR, NOT) affect the result.
Basic Logic Values
- True (T) = 1
- False (F) = 0
Common Logical Operators
| Operator | Symbol | Meaning |
|---|---|---|
| NOT | ¬ or ~ | Reverses the truth value |
| AND | ∧ | True only if both values are true |
| OR | ∨ | True if at least one is true |
Truth Tables for Basic Operations
A. NOT (¬A)
| A | ¬A |
|---|---|
| T | F |
| F | T |
B. AND (A ∧ B)
| A | B | A ∧ B |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
C. OR (A ∨ B)
| A | B | A ∨ B |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Constructing a Truth Table
- Step 1: List all possible combinations of truth values for variables (A, B, etc.)
- Step 2: Apply logical operators step by step.
- Step 3: Show the final result for each row.
Why Are Truth Tables Important?
- They help visualize and verify logical expressions.
- Useful in math, computer science, and digital circuits.
- Helps determine if a statement is always true (tautology), always false (contradiction), or sometimes true (contingency).
Example: (A ∨ B) ∧ ¬A
| A | B | A ∨ B | ¬A | (A ∨ B) ∧ ¬A |
|---|---|---|---|---|
| T | T | T | F | F |
| T | F | T | F | F |
| F | T | T | T | T |
| F | F | F | T | F |
Learn with an example
🎈 Complete the truth table.
| p | q | p∨q |
| T | T | |
| T | F | |
| F | T | |
| F | F | F |
- Fill in the third column. Determine if the value of either p or q is true.
| p | q | p∨q |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
🎈 Complete the truth table.
| q | r | r∧q |
| T | T | |
| T | F | F |
| F | T | |
| F | F |
- Fill in the third column. Determine if the values of both r and q are true.
| q | r | r∧q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
🎈Complete the truth table.
| q | r | r∧q |
| T | T | T |
| T | F | |
| F | T | |
| F | F |
- Fill in the third column. Determine if the values of both r and q are true.
| q | r | r∧q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Let’s practice!🖊️
