Truth table for (A↔B)

Simply enter your logical expression in the calculator input field and click calculate. The truth table will automatically be generated showing all possible combinations of variable values and the resulting output for your expression.

The variables are listed alphabetically, and the rows count through every assignment starting from all-false, with the first variable changing fastest, so the last row is the one where every variable is true. Textbooks differ here — many start from all-true instead — so the rows can appear in a different sequence from your course notes even though the table says exactly the same thing.

Two to the power of the number of distinct variables: three variables give eight rows, four give sixteen, ten give 1,024. Every variable you add doubles the table, which is why a long formula is usually easier to judge from the properties and the equivalent forms than by reading every row.

Yes. The notation toggle on the truth table switches between the ⊤ and ⊥ symbols and 1 and 0, and your choice is remembered in this browser the next time you visit.

Read the final column. If every row is true the formula is a tautology; if every row is false it is a contradiction; if the column has both it is contingent. It is satisfiable as soon as one row is true. The calculator states all of this above the table, so the column is a way to check the verdict rather than to work it out.