Exactamente una opción de pago: efectivo, tarjeta o vale
Exactamente uno entre efectivo, tarjeta o vale, escrito como tres términos mutuamente excluyentes. Ocho filas con tres válidas, una FNC de cuatro cláusulas que se lee como la política, y un mapa de Karnaugh con tres celdas aisladas.
Una caja acepta exactamente un método de pago, y la regla detalla las tres combinaciones permitidas: solo efectivo, solo tarjeta o solo vale, cada término nombrando los tres indicadores. La lectura del motor enumera esos tres casos. En la tabla de ocho filas sobre cash, card y voucher la salida es verdadera en tres filas, Σm(1, 2, 4), y falsa en las otras cinco, incluida la fila sin ningún método elegido y todas las filas con dos o tres.
Las comprobaciones: no es tautología, contraejemplo las tres entradas en FALSO; satisfacible, testigo cash = FALSO, card = FALSO, voucher = VERDADERO. El simplificador no encontró ninguna ley que acorte la expresión de catorce operadores; la FND son los tres términos originales. El conversor a FNC encuentra el enunciado más corto: (cash OR card OR voucher) AND (NOT cash OR NOT card) AND (NOT cash OR NOT voucher) AND (NOT card OR NOT voucher), cuatro cláusulas y nueve literales, que se lee como «al menos uno, y nunca dos juntos». El mapa dibuja tres grupos de una celda, tres implicantes primos. Compuertas: 40 NAND, 67 NOR.
Es la página de «exactamente uno» con nombres de negocio, y la FNC es la forma que conviene conservar: la primera cláusula es la validación de «elige un método», y las tres cláusulas de pares son las validaciones de «solo un método», cada una un mensaje de error aparte en un formulario. Lo que hay que vigilar es la selección vacía, que la regla rechaza en la fila 0; un sistema que por defecto no tiene método y se salta la validación cuando no se tocó nada admite esa fila por accidente. La página de «como máximo uno» muestra cómo queda la regla cuando el caso vacío se permite.
valid := (cash AND NOT card AND NOT voucher) OR (NOT cash AND card AND NOT voucher) OR (NOT cash AND NOT card AND voucher) · salida
Comprobaciones exactas
Tabla de verdad (8 filas)
| # | cash | card | voucher | valid |
|---|---|---|---|---|
| 0 | FALSO | FALSO | FALSO | FALSO |
| 1 | FALSO | FALSO | VERDADERO | VERDADERO |
| 2 | FALSO | VERDADERO | FALSO | VERDADERO |
| 3 | FALSO | VERDADERO | VERDADERO | FALSO |
| 4 | VERDADERO | FALSO | FALSO | VERDADERO |
| 5 | VERDADERO | FALSO | VERDADERO | FALSO |
| 6 | VERDADERO | VERDADERO | FALSO | FALSO |
| 7 | VERDADERO | VERDADERO | VERDADERO | FALSO |
Lectura en lenguaje claro
Principiantevalid es verdadero exactamente cuando se cumple al menos una de las condiciones siguientes (pueden cumplirse varias):
1. cash es verdadero, card es falso y voucher es falso
2. cash es falso, card es verdadero y voucher es falso
3. cash es falso, card es falso y voucher es verdadero
En todos los demás casos, valid es falso.
Sobre los operadores:
- OR (O) es inclusivo: es verdadero en cuanto al menos una parte es verdadera, también cuando lo son varias.
- AND (Y) solo es verdadero cuando todas sus partes son verdaderas.
- NOT (NO) invierte un valor: lo verdadero pasa a ser falso y lo falso, verdadero.
Intermediovalid es verdadero exactamente cuando se cumple al menos una de las condiciones siguientes (pueden cumplirse varias):
1. cash es verdadero, card es falso y voucher es falso
2. cash es falso, card es verdadero y voucher es falso
3. cash es falso, card es falso y voucher es verdadero
En todos los demás casos, valid es falso.
Avanzadovalid es verdadero exactamente cuando se cumple al menos una de las condiciones siguientes (pueden cumplirse varias) [disyunción inclusiva ∨]:
1. cash es verdadero, card es falso y voucher es falso [conjunción ∧]
2. cash es falso, card es verdadero y voucher es falso [conjunción ∧]
3. cash es falso, card es falso y voucher es verdadero [conjunción ∧]
En todos los demás casos, valid es falso.
Notación formal: (cash ∧ ¬card ∧ ¬voucher) ∨ (¬cash ∧ card ∧ ¬voucher) ∨ (¬cash ∧ ¬card ∧ voucher)
Diagrama lógico
Simplificación paso a paso
El motor no encontró ninguna ley que acorte esta expresión; ya es tan corta como sus leyes de reescritura permiten.
(cash AND NOT card AND NOT voucher) OR (NOT cash AND card AND NOT voucher) OR (NOT cash AND NOT card AND voucher)
Mapa de Karnaugh
- celdas m1
NOT cash AND NOT card AND voucher - celdas m2
NOT cash AND card AND NOT voucher - celdas m4
cash AND NOT card AND NOT voucher
Mintérminos y maxtérminos
valid(cash, card, voucher) = Σm(1, 2, 4)valid(cash, card, voucher) = ΠM(0, 3, 5, 6, 7)Orden de variables: cash, card, voucher · 8 filas
Formas normales
Forma normal conjuntiva (FNC)
(cash OR card OR voucher) AND (NOT cash OR NOT card) AND (NOT cash OR NOT voucher) AND (NOT card OR NOT voucher)4 cláusulas, 9 literales · complete · Distributividad ×2, Complemento ×5, Absorción ×5, Idempotencia ×1
Forma normal disyuntiva (FND)
(cash AND NOT card AND NOT voucher) OR (NOT cash AND card AND NOT voucher) OR (NOT cash AND NOT card AND voucher)3 términos, 9 literales · complete
Solo NAND, solo NOR
Forma solo con NAND
NAND(NAND(NAND(NAND(NAND(NAND(cash, NAND(card, card)), NAND(cash, NAND(card, card))), NAND(voucher, voucher)), NAND(NAND(NAND(NAND(cash, cash), card), NAND(NAND(cash, cash), card)), NAND(voucher, voucher))), NAND(NAND(NAND(NAND(cash, NAND(card, card)), NAND(cash, NAND(card, card))), NAND(voucher, voucher)), NAND(NAND(NAND(NAND(cash, cash), card), NAND(NAND(cash, cash), card)), NAND(voucher, voucher)))), NAND(NAND(NAND(NAND(cash, cash), NAND(card, card)), NAND(NAND(cash, cash), NAND(card, card))), voucher))40 compuertas · equivalencia verificada en todas las filas
Forma solo con NOR
NOR(NOR(NOR(NOR(NOR(NOR(NOR(NOR(cash, cash), card), NOR(NOR(cash, cash), card)), voucher), NOR(NOR(NOR(cash, NOR(card, card)), NOR(cash, NOR(card, card))), voucher)), NOR(NOR(NOR(NOR(NOR(cash, cash), card), NOR(NOR(cash, cash), card)), voucher), NOR(NOR(NOR(cash, NOR(card, card)), NOR(cash, NOR(card, card))), voucher))), NOR(NOR(NOR(cash, card), NOR(cash, card)), NOR(voucher, voucher))), NOR(NOR(NOR(NOR(NOR(NOR(NOR(cash, cash), card), NOR(NOR(cash, cash), card)), voucher), NOR(NOR(NOR(cash, NOR(card, card)), NOR(cash, NOR(card, card))), voucher)), NOR(NOR(NOR(NOR(NOR(cash, cash), card), NOR(NOR(cash, cash), card)), voucher), NOR(NOR(NOR(cash, NOR(card, card)), NOR(cash, NOR(card, card))), voucher))), NOR(NOR(NOR(cash, card), NOR(cash, card)), NOR(voucher, voucher))))67 compuertas · equivalencia verificada en todas las filas
La misma regla como código
Python
# -*- coding: utf-8 -*-
# Generated by Tangibool (tangibool.python/1). Do not edit by hand; regenerate from the source revision.
# Model: not stated
# Source revision: reference
# Interpretation status: not stated
"""Tangibool evaluator (decision model).
Generated deterministically from the validated Boolean model; it evaluates exactly that
model. It does not establish that the model is a complete, legal, or safe statement of a
real-world rule, and evaluating examples does not verify the rule.
Source revision: reference
Interpretation status: not stated
Exporter: 1.0.0 (format tangibool.python/1; engine 1.0.0; semantics tangibool-semantics/1)
Logic digest: 61dd28d6d3ab263c9e6d0b1c2132982144928c55e7d93bac9d3a8f60db77c999
Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78
Inputs (dict keys, declared order) and generated parameter names:
'cash' -> input_cash
'card' -> input_card
'voucher' -> input_voucher
Outputs (declared order) and their functions:
'valid' -> output_valid(inputs)
Assumptions (the declared scope, checked by in_scope(inputs)):
none; every complete assignment is in scope.
Input contract:
Every required input must be exactly True or False (type(value) is bool). Missing
inputs, None, strings, integers (including 0 and 1), and keys that are not declared
inputs raise InputError before anything is evaluated, including inputs that a
short-circuiting operator would never read. Results are always bool.
Scope:
Decision functions raise OutOfScopeError when the inputs violate an assumption; an
out-of-scope assignment is never turned into a False result. Pass check_scope=False
to evaluate without the scope check, and use in_scope(inputs) to test it separately.
Usage:
import tangibool_model as model
model.evaluate({'cash': False, 'card': False, 'voucher': False})
# -> {'valid': False}
model.output_valid({'cash': False, 'card': False, 'voucher': False})
# -> False
model.evaluate({'cash': 1, 'card': False, 'voucher': False})
# raises InputError: 1 is an int, not a bool
"""
import collections.abc as _abc
from typing import Dict, Mapping, Tuple
__all__ = [
"MODEL_INFO",
"IDENTIFIER_MAP",
"INPUT_NAMES",
"OUTPUT_NAMES",
"ASSUMPTIONS",
"InputError",
"OutOfScopeError",
"minterm_index",
"in_scope",
"evaluate",
"output_valid",
]
MODEL_INFO = {
"format": "tangibool.python/1",
"mode": "decision",
"model": None,
"revision": "reference",
"interpretation": None,
"exporter": "1.0.0",
"engine_version": "1.0.0",
"semantics_version": "tangibool-semantics/1",
"logic_digest": "61dd28d6d3ab263c9e6d0b1c2132982144928c55e7d93bac9d3a8f60db77c999",
"assumptions_digest": "d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78",
"primary_output": "valid",
"unused_inputs": (),
"subcircuits": (),
}
# Stable ID -> generated identifier (reversible mapping; names are exact, escaped strings).
IDENTIFIER_MAP = {
"v_be76c451838e": {"kind": "input", "name": "cash", "identifier": "input_cash"},
"v_c974ea178eba": {"kind": "input", "name": "card", "identifier": "input_card"},
"v_c205843e647b": {"kind": "input", "name": "voucher", "identifier": "input_voucher"},
"f_453ca86cbb3c": {"kind": "output", "name": "valid", "identifier": "output_valid"},
}
INPUT_NAMES = ("cash", "card", "voucher")
OUTPUT_NAMES = ("valid",)
ASSUMPTIONS = ()
_DECLARED_INPUTS = frozenset(INPUT_NAMES)
_SCOPE_INPUTS = ()
_ASSUMPTION_FORMULAS = {entry["name"]: entry["formula"] for entry in ASSUMPTIONS}
class InputError(ValueError):
"""Raised when inputs are missing, undeclared, or not exactly True/False.
Every required input must satisfy type(value) is bool. Missing inputs, None, strings,
integers (including 0 and 1), and keys that are not declared inputs are rejected before
anything is evaluated. A missing input is never treated as False. The individual problems
are listed in the problems attribute.
"""
def __init__(self, problems):
self.problems = tuple(problems)
super().__init__("Invalid inputs: " + "; ".join(self.problems))
class OutOfScopeError(ValueError):
"""Raised when the inputs violate the model's assumptions (its declared scope).
Outside its assumptions the rule has no decision: this error is never a False result.
The names of the violated assumptions are in the violated attribute.
"""
def __init__(self, violated):
self.violated = tuple(violated)
details = ", ".join(name + " (" + _ASSUMPTION_FORMULAS.get(name, "?") + ")" for name in self.violated)
super().__init__(
"Out of scope: the inputs violate "
+ ("assumption " if len(self.violated) == 1 else "assumptions ")
+ details
+ ". The rule has no decision outside its assumptions; this is not a False result."
)
def _short_repr(value: object) -> str:
text = repr(value)
return text if len(text) <= 60 else text[:57] + "..."
def _checked_inputs(inputs: Mapping[str, bool], required: Tuple[str, ...], check_scope: bool) -> Dict[str, bool]:
"""Validate inputs strictly before anything is evaluated and return a plain copy."""
if type(check_scope) is not bool:
raise TypeError("check_scope must be True or False")
if not isinstance(inputs, _abc.Mapping):
raise InputError(["inputs must be a mapping from input names to True/False, got " + type(inputs).__name__])
problems = []
for key in inputs:
if type(key) is not str or key not in _DECLARED_INPUTS:
declared = ", ".join(repr(name) for name in INPUT_NAMES) or "none"
problems.append("undeclared input " + _short_repr(key) + " (declared inputs: " + declared + ")")
needed = tuple(required) + (_SCOPE_INPUTS if check_scope else ())
for name in needed:
if name not in inputs:
problems.append("missing required input " + repr(name))
for key, value in inputs.items():
if type(key) is str and key in _DECLARED_INPUTS and type(value) is not bool:
problems.append(
"input " + repr(key) + " must be True or False (type bool), got "
+ type(value).__name__ + " " + _short_repr(value)
)
if problems:
raise InputError(list(dict.fromkeys(problems)))
return dict(inputs.items())
def _require_bool_args(function: str, pairs: Tuple[Tuple[str, object], ...]) -> None:
problems = [
"argument " + repr(name) + " of " + function + " must be True or False (type bool), got "
+ type(value).__name__ + " " + _short_repr(value)
for name, value in pairs
if type(value) is not bool
]
if problems:
raise InputError(problems)
def minterm_index(*values: bool) -> int:
"""Row index of an assignment over a declared variable order.
The first value is the most significant bit, so all-False is row 0. Used for indexed
minterm (sum) and maxterm (product) forms.
"""
index = 0
for value in values:
if type(value) is not bool:
raise InputError(["minterm_index() takes True/False values, got " + type(value).__name__ + " " + _short_repr(value)])
index = index * 2 + (1 if value else 0)
return index
def _scope_values(values: Dict[str, bool]) -> Tuple[Tuple[str, bool], ...]:
"""Value of every enabled, confirmed assumption for validated inputs, in declared order."""
return ()
def _require_in_scope(values: Dict[str, bool]) -> None:
violated = tuple(name for name, holds in _scope_values(values) if not holds)
if violated:
raise OutOfScopeError(violated)
def in_scope(inputs: Mapping[str, bool]) -> bool:
"""True when the inputs satisfy every assumption (the model's declared scope).
Requires the inputs the assumptions read; raises InputError for invalid inputs.
"""
values = _checked_inputs(inputs, (), True)
return all(holds for _, holds in _scope_values(values))
# ---- Formula bodies (inputs are validated by the public functions below) ----
def _compute_output_valid(input_cash: bool, input_card: bool, input_voucher: bool) -> bool:
"""Decision output 'valid': (cash AND NOT card AND NOT voucher) OR (NOT cash AND card AND NOT voucher) OR (NOT cash AND NOT card AND voucher)"""
return (input_cash and (not input_card) and (not input_voucher)) or ((not input_cash) and input_card and (not input_voucher)) or ((not input_cash) and (not input_card) and input_voucher)
# ---- Public API ----
def output_valid(inputs: Mapping[str, bool], *, check_scope: bool = True) -> bool:
"""Decision output 'valid' (stable ID f_453ca86cbb3c).
'valid' := (cash AND NOT card AND NOT voucher) OR (NOT cash AND card AND NOT voucher) OR (NOT cash AND NOT card AND voucher)
Required inputs: 'cash', 'card', 'voucher'.
Raises InputError for missing, undeclared, or non-bool inputs, and OutOfScopeError
when check_scope is True and the inputs violate an assumption.
"""
values = _checked_inputs(inputs, ("cash", "card", "voucher"), check_scope)
if check_scope:
_require_in_scope(values)
output_valid_value = _compute_output_valid(values["cash"], values["card"], values["voucher"])
return output_valid_value
def evaluate(inputs: Mapping[str, bool], *, check_scope: bool = True) -> Dict[str, bool]:
"""Evaluate every output (declared order); each output is computed once.
Required inputs: 'cash', 'card', 'voucher'.
Raises InputError for missing, undeclared, or non-bool inputs, and OutOfScopeError
when check_scope is True and the inputs violate an assumption.
"""
values = _checked_inputs(inputs, ("cash", "card", "voucher"), check_scope)
if check_scope:
_require_in_scope(values)
output_valid_value = _compute_output_valid(values["cash"], values["card"], values["voucher"])
return {
"valid": output_valid_value,
}
PostgreSQL
-- Tangibool PostgreSQL export (tangibool.postgresql/1)
-- Target: PostgreSQL 16 or later with typed boolean inputs; tested with PostgreSQL 18.3 (PGlite 0.5.8).
-- Not a claim of compatibility with other SQL dialects.
-- Model: not stated
-- Source revision: reference
-- Interpretation status: not stated
-- Exporter: 1.0.0 (engine 1.0.0; semantics tangibool-semantics/1)
-- Logic digest: 61dd28d6d3ab263c9e6d0b1c2132982144928c55e7d93bac9d3a8f60db77c999
-- Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78
-- Mode: decision
--
-- Read-only: this file contains only WITH / VALUES / SELECT statements. No DDL, DML,
-- procedures, credentials, network access, or database changes. The expressions are pure
-- Boolean expressions, so their result does not depend on SQL evaluation order.
--
-- NON-NULL INPUT PRECONDITION: NULL is not a truth value of this rule. Every fragment below
-- is defined only when every input column it reads is a non-NULL boolean. The guard template
-- (section 2) marks any NULL input as 'invalid_input' and any row that violates the
-- assumptions as 'out_of_scope', and fills output columns only for 'ok' rows; a NULL in an
-- output column of another row is an envelope marker, not a third truth value. Never wrap
-- the fragments in COALESCE(..., FALSE) or otherwise choose a meaning for unknown inputs.
-- This evaluates the supplied model; it does not show that the model is a complete, legal,
-- or safe statement of a real-world rule.
--
-- Input columns (stable ID: name -> column):
-- v_be76c451838e: cash -> "in_cash"
-- v_c974ea178eba: card -> "in_card"
-- v_c205843e647b: voucher -> "in_voucher"
-- Output columns:
-- f_453ca86cbb3c: valid -> "out_valid"
-- Assumptions (scope K; exported separately and never folded into an output):
-- none; every complete input row is in scope.
-- ----------------------------------------------------------------------------------------------
-- 1. Expression fragments (parenthesised; non-NULL boolean inputs required)
-- ----------------------------------------------------------------------------------------------
--
-- [out_valid] output valid (stable ID f_453ca86cbb3c)
-- valid := (cash AND NOT card AND NOT voucher) OR (NOT cash AND card AND NOT voucher) OR (NOT cash AND NOT card AND voucher)
-- PRECONDITION: "in_cash", "in_card", "in_voucher" are non-NULL booleans.
-- (("in_cash" AND (NOT "in_card") AND (NOT "in_voucher")) OR ((NOT "in_cash") AND "in_card" AND (NOT "in_voucher")) OR ((NOT "in_cash") AND (NOT "in_card") AND "in_voucher"))
--
-- ----------------------------------------------------------------------------------------------
-- 2. Guard template (read-only SELECT over an inputs list)
-- ----------------------------------------------------------------------------------------------
-- Replace the example rows between the markers with your own rows, or replace the inputs
-- CTE with a SELECT that provides the boolean columns listed in the header. status is
-- 'invalid_input' when any input is NULL, 'out_of_scope' when the assumptions are false, and
-- 'ok' otherwise; output columns are filled only for 'ok' rows (NULL elsewhere is an
-- envelope marker). Assumption columns are shown for rows with complete inputs.
WITH inputs ("row_id", "in_cash", "in_card", "in_voucher") AS (
-- tangibool:example-rows:begin
VALUES
(1, FALSE, FALSE, FALSE),
(2, FALSE, FALSE, TRUE),
(3, FALSE, TRUE, FALSE),
(4, FALSE, TRUE, TRUE),
(5, TRUE, FALSE, FALSE),
(6, TRUE, FALSE, TRUE),
(7, TRUE, TRUE, FALSE),
(8, TRUE, TRUE, TRUE),
(9, NULL::boolean, FALSE, FALSE)
-- tangibool:example-rows:end
),
checked AS (
SELECT
inputs.*,
CASE
WHEN "in_cash" IS NULL OR "in_card" IS NULL OR "in_voucher" IS NULL THEN 'invalid_input'
ELSE 'ok'
END AS "status"
FROM inputs
)
SELECT
"row_id",
"in_cash",
"in_card",
"in_voucher",
"status",
CASE WHEN "status" = 'ok' THEN (("in_cash" AND (NOT "in_card") AND (NOT "in_voucher")) OR ((NOT "in_cash") AND "in_card" AND (NOT "in_voucher")) OR ((NOT "in_cash") AND (NOT "in_card") AND "in_voucher")) END AS "out_valid"
FROM checked
ORDER BY "row_id";
SMT-LIB
; Tangibool SMT-LIB export (tangibool.smtlib/1) ; Profile: SMT-LIB 2.6 Boolean subset (QF_UF): Bool constants, define-fun, let, push/pop, assert, check-sat, echo. ; Tested with Z3 5.1.0 (z3-solver 5.2.0, WebAssembly build). ; Model: not stated ; Source revision: reference ; Interpretation status: not stated ; Exporter: 1.0.0 (engine 1.0.0; semantics tangibool-semantics/1) ; Logic digest: 61dd28d6d3ab263c9e6d0b1c2132982144928c55e7d93bac9d3a8f60db77c999 ; Assumptions digest: d58ee1ad38e23e5093e4baa1047b5ae70d6972e08f555e34ac3fa16df63c4a78 ; Mode: decision ; ; Reading results: each query block states what sat and unsat mean for its question. A sat ; answer comes with a witness or counterexample (ask for it with (get-model) after sat only); ; unsat settles that scoped query and is solver-checked, not an independently checked proof ; certificate; unknown settles nothing. Blocks are scoped with push/pop, so assertions never ; accumulate across questions. This checks the supplied model, not whether it is a complete, ; legal, or safe statement of a real-world rule. ; ; Symbols (stable ID: name -> symbol): ; v_be76c451838e: cash -> in_cash ; v_c974ea178eba: card -> in_card ; v_c205843e647b: voucher -> in_voucher ; f_453ca86cbb3c: valid -> out_valid (set-option :produce-models true) (set-info :smt-lib-version 2.6) (set-logic QF_UF) ; ---- Inputs (declared order) (declare-const in_cash Bool) ; cash (declare-const in_card Bool) ; card (declare-const in_voucher Bool) ; voucher ; ---- Outputs (dependencies first) ; output valid (stable ID f_453ca86cbb3c): (cash AND NOT card AND NOT voucher) OR (NOT cash AND card AND NOT voucher) OR (NOT cash AND NOT card AND voucher) (define-fun out_valid () Bool (or (and in_cash (not in_card) (not in_voucher)) (and (not in_cash) in_card (not in_voucher)) (and (not in_cash) (not in_card) in_voucher))) ; ---- Assumptions (the scope K; never folded into an output) ; K: conjunction of the enabled, confirmed assumptions (true when there are none) (define-fun K () Bool true) ; ---- Definitions only: nothing is asserted and no check is run. ; Add (assert ...) and (check-sat) inside (push 1) ... (pop 1) to ask a question.
LaTeX
valid = \left(\mathit{cash} \cdot \overline{\mathit{card}} \cdot \overline{\mathit{voucher}}\right) + \left(\overline{\mathit{cash}} \cdot \mathit{card} \cdot \overline{\mathit{voucher}}\right) + \left(\overline{\mathit{cash}} \cdot \overline{\mathit{card}} \cdot \mathit{voucher}\right)El error habitual
Escribir la regla como cash XOR card XOR voucher. Coincide en siete filas y difiere en cash = VERDADERO, card = VERDADERO, voucher = VERDADERO, donde la cadena de XOR es verdadera y la política dice que no. Una caja que deje marcar las tres opciones cobraría o abonaría de forma no especificada; la página de «exactamente uno» muestra esa fila.
Preguntas
¿Por qué la FNC tiene menos operadores pero el mismo número de literales?
Los tres términos de la FND repiten cada uno los tres indicadores, nueve literales; la FNC gasta sus nueve literales en una cláusula de tres literales y tres de dos. El conversor cuenta las dos formas, y la tabla confirma que son iguales en las ocho filas. Cuál es más corta depende de qué se cuente.
Relacionado
Operadores y compuertas
- Compuerta NOT (inversor): tabla de verdad, símbolo y el operador NOT
- Compuerta AND (puerta Y): tabla de verdad de 2, 3 y 4 entradas, símbolo y expresión
- Compuerta OR (puerta O): tabla de verdad de 2, 3 y 4 entradas
Herramientas
- Generador de tablas de verdad: cualquier expresión booleana, hasta 12 variables, con columnas intermedias
- Calculadora y simplificador de álgebra de Boole paso a paso (cada ley nombrada y verificada)
- Solucionador de mapas de Karnaugh: de 2 a 4 variables, agrupaciones, SOP y POS
Véase también
- Exactamente uno de tres: por qué XOR no sirve
- Como máximo uno de tres: exclusión mutua
- XOR de tres entradas es paridad impar, no «exactamente uno»
- Conversor a FNC y FND: formas normales conjuntiva y disyuntiva, mintérminos y maxtérminos
- Escribir reglas de negocio en lenguaje claro que se traduzcan a lógica
- Forma normal conjuntiva (FNC): definición, ejemplo y equivalente en inglés
Ejemplos resueltos
Generado a partir del motor de Tangibool, semántica tangibool-semantics/1, motor 1.0.0, compilación . Cada tabla, mapa, simplificación y veredicto de estas páginas lo calculó el motor de Tangibool al compilar el sitio, y cada afirmación la volvió a comprobar el mismo verificador exacto que usa la app. Los límites se indican donde aplican. © 2026 Foreranger LTD.