Interactive Truth Table Calculator
What is a Truth Table Calculator?
A truth table calculator is a tool that generates truth tables for logical expressions in propositional logic. Propositional logic deals with statements that are either true or false. Truth tables show all possible combinations of truth values for the variables in an expression and the resulting truth value of the expression.
These tables are essential in mathematics, computer science, digital logic design, and philosophy for analyzing logical arguments and designing circuits.
How to Use the Calculator
- Enter your logical expression using variables (A, B, C, etc.) and operators.
- Select the number of variables in your expression.
- Click "Generate Truth Table" to see the complete table.
- Interpret the results: each row shows a combination of inputs and the output.
Logical Operators
AND (∧ or &&)
| A | B | A ∧ B |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
OR (∨ or ||)
| A | B | A ∨ B |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
NOT (¬ or !)
| A | ¬A |
|---|---|
| T | F |
| F | T |
IMPLIES (→)
| A | B | A → B |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
BICONDITIONAL (↔)
| A | B | A ↔ B |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
XOR (^)
| A | B | A ^ B |
|---|---|---|
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | F |
Examples
2-Variable Example: A ∧ B
| A | B | A ∧ B |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
3-Variable Example: (A ∨ B) → C
| A | B | C | (A ∨ B) → C |
|---|---|---|---|
| T | T | T | T |
| T | T | F | F |
| T | F | T | T |
| T | F | F | F |
| F | T | T | T |
| F | T | F | F |
| F | F | T | T |
| F | F | F | T |
Compound Statement: ¬(A ∧ B) ∨ (C → D)
This combines negation, conjunction, disjunction, and implication.
Use Cases
- Students: Learn discrete mathematics and logical reasoning.
- Programmers: Understand boolean logic in coding.
- Digital Logic Designers: Design and verify circuits.
- Boolean Simplification: Minimize logical expressions.
Frequently Asked Questions
What is propositional logic?
Propositional logic is a branch of logic that deals with propositions that can be either true or false.
How many variables can I use?
Our calculator supports up to 5 variables, generating up to 32 rows.
What operators are supported?
AND (&&, ∧), OR (||, ∨), NOT (!, ¬), IMPLIES (->), BICONDITIONAL (<->), XOR (^).
Can I use parentheses?
Yes, use parentheses to group expressions and control evaluation order.
What if my expression is invalid?
The calculator will attempt to evaluate it. Check your syntax if results seem wrong.
Is this tool free?
Yes, completely free to use.