RandoziTruth Table Generator
Type a logic expression such as (A and B) -> C and see every row of its truth table, instantly and in your browser.
Verdict
Depends on the values
7 of 8 rows are true.
| A | B | C | Result |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 0 | 1 | 1 |
| 0 | 0 | 0 | 1 |
How it works
- Type an expression using letters or short names for the variables, for example (A or B) and not C.
- Use and, or, not, xor, -> for implication and <-> for “if and only if”. Symbols such as & | ! ^ work too.
- Read the table, one row per combination, and the verdict: always true, always false, or depends on the values.
- Type a second expression in the comparison box to check that two formulas are equivalent, or copy the table as CSV.
What people use it for
Logic homework
Check a hand-built table for a proposition with three variables.
Simplifying conditions
Confirm that !(A && B) behaves like !A || !B before changing an if statement.
Digital circuits
List when a gate network outputs 1, then copy the table into your notes.
Questions
- In which order are the operators applied?
- From strongest to weakest: not, and, xor, or, implies, then if and only if. Implication groups to the right, so A -> B -> C reads as A -> (B -> C). When in doubt, add parentheses.
- How many variables are supported?
- Up to 8, which is 256 rows. Variables are names made of letters, digits and underscores, and they are case-sensitive: A and a are two variables. The words and, or, not, xor, implies, iff, true and false are reserved. The values 0 and 1 are accepted as constants. Very long or deeply nested expressions are refused with a message.
- How does the equivalence check work?
- Both expressions are evaluated for every combination of all the variables found in either one. They are equivalent when the results match on every row; a variable that appears in only one expression is still tried with both values.