Sr Examen
Expresión xv(x^(y→w))*v*(¬y^z)*v¬w
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
x∨(¬w)∨(z∧(¬y))∨(x∧(y⇒w))
$$x \vee \left(x \wedge \left(y \Rightarrow w\right)\right) \vee \left(z \wedge \neg y\right) \vee \neg w$$
Solución detallada
$$y \Rightarrow w = w \vee \neg y$$
$$x \wedge \left(y \Rightarrow w\right) = x \wedge \left(w \vee \neg y\right)$$
$$x \vee \left(x \wedge \left(y \Rightarrow w\right)\right) \vee \left(z \wedge \neg y\right) \vee \neg w = x \vee \left(z \wedge \neg y\right) \vee \neg w$$
$$x \wedge \left(y \Rightarrow w\right) = x \wedge \left(w \vee \neg y\right)$$
$$x \vee \left(x \wedge \left(y \Rightarrow w\right)\right) \vee \left(z \wedge \neg y\right) \vee \neg w = x \vee \left(z \wedge \neg y\right) \vee \neg w$$
Tabla de verdad
+---+---+---+---+--------+ | w | x | y | z | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+
FNCD
[src]
$$\left(x \vee z \vee \neg w\right) \wedge \left(x \vee \neg w \vee \neg y\right)$$
(x∨z∨(¬w))∧(x∨(¬w)∨(¬y))
FND
[src]
Ya está reducido a FND
$$x \vee \left(z \wedge \neg y\right) \vee \neg w$$
x∨(¬w)∨(z∧(¬y))
FNC
[src]
$$\left(x \vee z \vee \neg w\right) \wedge \left(x \vee \neg w \vee \neg y\right)$$
(x∨z∨(¬w))∧(x∨(¬w)∨(¬y))