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Lógica matemática/ (xvy)->(x&z)

Expresión (xvy)->(x&z)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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