Sr Examen
Lógica matemática/ xzv((w⇒x)~(z⇒y))

Expresión xzv((w⇒x)~(z⇒y))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (x∧z)∨((w⇒x)⇔(z⇒y))
    $$\left(x \wedge z\right) \vee \left(\left(w \Rightarrow x\right) ⇔ \left(z \Rightarrow y\right)\right)$$
    Solución detallada
    $$w \Rightarrow x = x \vee \neg w$$
    $$z \Rightarrow y = y \vee \neg z$$
    $$\left(w \Rightarrow x\right) ⇔ \left(z \Rightarrow y\right) = \left(x \wedge y\right) \vee \left(x \wedge \neg z\right) \vee \left(y \wedge \neg w\right) \vee \left(\neg w \wedge \neg z\right) \vee \left(w \wedge z \wedge \neg x \wedge \neg y\right)$$
    $$\left(x \wedge z\right) \vee \left(\left(w \Rightarrow x\right) ⇔ \left(z \Rightarrow y\right)\right) = x \vee \left(y \wedge \neg w\right) \vee \left(\neg w \wedge \neg z\right) \vee \left(w \wedge z \wedge \neg y\right)$$
    Simplificación [src]
    $$x \vee \left(y \wedge \neg w\right) \vee \left(\neg w \wedge \neg z\right) \vee \left(w \wedge z \wedge \neg y\right)$$ 
    x∨(y∧(¬w))∨((¬w)∧(¬z))∨(w∧z∧(¬y))
    Tabla de verdad 
    +---+---+---+---+--------+
| w | x | y | z | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 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      |
+---+---+---+---+--------+
    FNC [src]
    $$\left(w \vee x \vee \neg w\right) \wedge \left(x \vee z \vee \neg w\right) \wedge \left(x \vee \neg w \vee \neg y\right) \wedge \left(w \vee x \vee y \vee \neg w\right) \wedge \left(w \vee x \vee y \vee \neg z\right) \wedge \left(w \vee x \vee \neg w \vee \neg z\right) \wedge \left(x \vee y \vee z \vee \neg w\right) \wedge \left(x \vee y \vee z \vee \neg z\right) \wedge \left(x \vee y \vee \neg w \vee \neg y\right) \wedge \left(x \vee y \vee \neg y \vee \neg z\right) \wedge \left(x \vee z \vee \neg w \vee \neg z\right) \wedge \left(x \vee \neg w \vee \neg y \vee \neg z\right)$$ 
    (w∨x∨(¬w))∧(x∨z∨(¬w))∧(x∨(¬w)∨(¬y))∧(w∨x∨y∨(¬w))∧(w∨x∨y∨(¬z))∧(x∨y∨z∨(¬w))∧(x∨y∨z∨(¬z))∧(w∨x∨(¬w)∨(¬z))∧(x∨y∨(¬w)∨(¬y))∧(x∨y∨(¬y)∨(¬z))∧(x∨z∨(¬w)∨(¬z))∧(x∨(¬w)∨(¬y)∨(¬z))
    FNDP [src]
    $$x \vee \left(y \wedge \neg w\right) \vee \left(\neg w \wedge \neg z\right) \vee \left(w \wedge z \wedge \neg y\right)$$ 
    x∨(y∧(¬w))∨((¬w)∧(¬z))∨(w∧z∧(¬y))
    FNCD [src]
    $$\left(x \vee z \vee \neg w\right) \wedge \left(x \vee \neg w \vee \neg y\right) \wedge \left(w \vee x \vee y \vee \neg z\right)$$ 
    (x∨z∨(¬w))∧(x∨(¬w)∨(¬y))∧(w∨x∨y∨(¬z))
    FND [src]
    Ya está reducido a FND
    $$x \vee \left(y \wedge \neg w\right) \vee \left(\neg w \wedge \neg z\right) \vee \left(w \wedge z \wedge \neg y\right)$$ 
    x∨(y∧(¬w))∨((¬w)∧(¬z))∨(w∧z∧(¬y))
    © Sr Examen