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Lógica matemática/ xy+((x→z)≡(y→w))

Expresión xy+((x→z)≡(y→w))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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