1
Write the claim with variables
Replace each simple statement with a letter such as P, Q, or R, then connect them with logical operators.
Free propositional logic tool
Free Truth Table Generator
A truth table generator evaluates a logic expression across every true and false input combination. Use it to test implications, equivalence, contradictions, and debate claims that depend on precise reasoning.
Enter expressions with ! for not, & for and, | for or, -> for implication, and <-> for equivalence.
AND, OR, NOTImplication and equivalenceCSV copy
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Expression builder
Test a logic expression
Operators
Examples
Truth table
Tautology
PQ
| P | Q | (P -> Q) <-> (!Q -> !P) |
|---|---|---|
| F | F | T |
| F | T | T |
| T | F | T |
| T | T | T |
Method
How to read the result
The final column is the full expression. Mixed true and false rows mean the claim depends on the facts assigned to each variable.
2
Generate every truth assignment
The table lists each possible true and false combination for the variables in the expression.
3
Check the final column
If every row is true, the expression is a tautology. If every row is false, it is a contradiction. Mixed rows are contingent.
Truth table questions
What is a truth table generator?
A truth table generator evaluates a logical expression across every possible combination of true and false inputs so you can see exactly when the claim holds.
Which logic operators does this tool support?
The tool supports not with !, and with &, or with |, implication with ->, and biconditional equivalence with <->.
What does tautology mean in a truth table?
A tautology is an expression that is true on every row of the truth table, no matter how the variables are assigned.
How is implication evaluated?
P -> Q is false only when P is true and Q is false. In every other row, the implication is true.
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