Sr Examen
Expresión {(\neg{A}\lor{A})\land(1\lor0)\lor(0\land1)}(¬A∨A)∧(1∨0)∨(0∧1)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(a∨(¬a))∧(((a∧e∧g∧n)|(a∨l))|(l∧(1|l))|(l∨(0|l)))
$$\left(\left(\left(a \wedge e \wedge g \wedge n\right) | \left(a \vee l\right)\right) | \left(l \wedge \left(1 | l\right)\right) | \left(l \vee \left(0 | l\right)\right)\right) \wedge \left(a \vee \neg a\right)$$
Solución detallada
$$a \vee \neg a = 1$$
$$\left(a \wedge e \wedge g \wedge n\right) | \left(a \vee l\right) = \neg a \vee \neg e \vee \neg g \vee \neg n$$
$$1 | l = \neg l$$
$$l \wedge \left(1 | l\right) = \text{False}$$
$$0 | l = 1$$
$$l \vee \left(0 | l\right) = 1$$
$$\left(\left(a \wedge e \wedge g \wedge n\right) | \left(a \vee l\right)\right) | \left(l \wedge \left(1 | l\right)\right) | \left(l \vee \left(0 | l\right)\right) = 1$$
$$\left(\left(\left(a \wedge e \wedge g \wedge n\right) | \left(a \vee l\right)\right) | \left(l \wedge \left(1 | l\right)\right) | \left(l \vee \left(0 | l\right)\right)\right) \wedge \left(a \vee \neg a\right) = 1$$
$$\left(a \wedge e \wedge g \wedge n\right) | \left(a \vee l\right) = \neg a \vee \neg e \vee \neg g \vee \neg n$$
$$1 | l = \neg l$$
$$l \wedge \left(1 | l\right) = \text{False}$$
$$0 | l = 1$$
$$l \vee \left(0 | l\right) = 1$$
$$\left(\left(a \wedge e \wedge g \wedge n\right) | \left(a \vee l\right)\right) | \left(l \wedge \left(1 | l\right)\right) | \left(l \vee \left(0 | l\right)\right) = 1$$
$$\left(\left(\left(a \wedge e \wedge g \wedge n\right) | \left(a \vee l\right)\right) | \left(l \wedge \left(1 | l\right)\right) | \left(l \vee \left(0 | l\right)\right)\right) \wedge \left(a \vee \neg a\right) = 1$$
Tabla de verdad
+---+---+---+---+---+--------+ | a | e | g | l | n | result | +===+===+===+===+===+========+ | 0 | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 0 | 0 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+---+--------+