Truth Table Generator
Generate a complete truth table for a boolean expression with AND, OR, NOT, XOR and implies.
About Truth Table Generator
A truth table lists all possible combinations of truth values for the variables in a boolean expression and evaluates the expression for each. It can reveal whether an expression is a tautology (always true), contradiction (always false), or contingency.
Formula
Row Count
Rows = 2^n where n is the number of variables
- n
- Number of distinct variables
Worked example
With the default values below, Truth Table Generator returns Truth Table Rows of 8. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Boolean Expression
- (A AND B) OR (NOT C)
Results
- Truth Table Rows
- 8
- Variables Found
- A, B, C
- Truth Table
- A | B | C | Result ------------------ F | F | F | T F | F | T | F F | T | F | T F | T | T | F T | F | F | T T | F | T | F T | T | F | T T | T | T | T
- Is Tautology?
- No
- Is Contradiction?
- No
Step by step
- 1Values used
- 2Row Count
- 3Truth Table Rows= 8
- 4Variables Found= A, B, C
- 5Truth Table= A | B | C | Result ------------------ F | F | F | T F | F | T | F F | T | F | T F | T | T | F T | F | F | T T | F | T | F T | T | F | T T | T | T | T
- 6Is Tautology?= No
- 7Is Contradiction?= No
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What operators are supported?
AND (conjunction), OR (disjunction), NOT (negation), XOR (exclusive or), and IMPLIES (material conditional). Use parentheses for grouping.
What is a tautology?
An expression that evaluates to true for every possible combination of variable values, e.g., 'A OR NOT A'.