Truth tables
Enter a propositional formula and see every row. Each subformula gets its own column, and the finished table exports as for your notes.
Tautology 4 rows ·
2 variables
| p | q | p → q | (p → q) ∧ p | ((p → q) ∧ p) → q |
|---|---|---|---|---|
| F | F | T | F | T |
| F | T | T | F | T |
| T | F | F | F | T |
| T | T | T | T | T |
Every row is true, so the formula is a tautology.
Reading the table
The first columns list every assignment of truth values to the propositional variables. The remaining columns evaluate each distinct subformula from the inside out; the last column is the whole formula.
A formula with a true final column in every row is a tautology. One with a false final column in every row is a contradiction. Anything else is contingent.
Syntax
- Negation:
~por!p. - Conjunction:
p & q. - Exclusive or:
p ^ q. - Disjunction:
p | qorp v q. - Implication:
p -> q. - Equivalence:
p <-> q. - Use parentheses to group;
~binds tightest, then&,|,->, and<->.
Export
The tab previews the document and lets you copy or download the .tex source. It uses amsmath,amssymb and array, so a standard TeX installation compiles the table.