AB is one name, not A AND B: implicit multiplication
AB is one name, not A AND B. Textbooks drop the dot in A·B; the parser does not, because a rule's inputs have names like member and banned, and AB must be allowed to be one of them.
The parser's diagnostic for A B is recorded below: a missing operator between A and B, with the note that implicit multiplication is not supported and the two repairs, insert AND or insert OR. AB with no space is not even that; it is a single identifier, and if no input of that name exists it becomes a new one, which is the quieter and worse failure.
The algebra notation has a product sign for exactly this reason: A·B (also A⋅B) is accepted and printed, and A'B' must be written A'·B'. The habit of juxtaposition comes from hand-written Boolean algebra, where variables are single letters and the dot is tedious. In a language with multi-letter names, juxtaposition is ambiguous, and the engine's parser is designed to refuse ambiguity rather than resolve it silently.
When copying an expression from a textbook, insert the dots or the word AND, and check the printed algebra form on the page: it shows A·B where it read a product and AB where it read a name.
What the parser says
| You typed | Code | Why it is rejected | Repair offered |
|---|---|---|---|
| A B | missing-operator | Missing operator between `A` and `B`. Implicit multiplication is not supported — write the operator explicitly. | Insert AND Insert OR |
The common slip
Pasting AB + A'C from a worked problem. AB becomes one unknown input and A'C another, and the formula has four variables instead of three. The truth table's variable list reveals it immediately.
Questions
Why not treat juxtaposition as AND when the names are single letters?
Because the rule would then change meaning when a name grows: AB is a product today and a name tomorrow. A language that keeps IDs stable across edits cannot afford a reading that depends on name length.
Which product signs are accepted?
The middle dot ·, the dot operator ⋅, the word AND, the symbol ∧ and the programming &&. The asterisk * is rejected with a repair, because it is arithmetic.
Related
Tools
- Logical equivalence checker: two expressions, exact verdict, counterexample
- Truth table generator: any Boolean expression, up to 12 variables, with intermediate columns
See also
- Logic symbols: meanings, LaTeX, Unicode and how to type them
- AND gate: truth table for 2, 3 and 4 inputs, symbol and expression
- Confusable names: l, 1, I, O and 0 in variable names
- Single & and | are bitwise in most languages
- Huntington's postulates of Boolean algebra, with their duals
Pitfalls
Generated from the Tangibool engine, semantics tangibool-semantics/1, engine 1.0.0, build . Every table, map, simplification and verdict on these pages was computed by the Tangibool engine when the site was built, and every claim was re-checked by the same exact checker the app uses. Limits are stated where they apply. © 2026 Foreranger LTD.