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Lógica matemática/ не((неx^неy)->(xv(z^неt)))

Expresión не((неx^неy)->(xv(z^неt)))

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    Solución

    Ha introducido [src] 
    ¬(((¬x)∧(¬y))⇒(x∨(z∧(¬t))))
    $$\left(\neg x \wedge \neg y\right) \not\Rightarrow \left(x \vee \left(z \wedge \neg t\right)\right)$$
    Solución detallada
    $$\left(\neg x \wedge \neg y\right) \Rightarrow \left(x \vee \left(z \wedge \neg t\right)\right) = x \vee y \vee \left(z \wedge \neg t\right)$$
    $$\left(\neg x \wedge \neg y\right) \not\Rightarrow \left(x \vee \left(z \wedge \neg t\right)\right) = \neg x \wedge \neg y \wedge \left(t \vee \neg z\right)$$
    Simplificación [src]
    $$\neg x \wedge \neg y \wedge \left(t \vee \neg z\right)$$ 
    (¬x)∧(¬y)∧(t∨(¬z))
    Tabla de verdad 
    +---+---+---+---+--------+
| t | x | y | z | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
    FNDP [src]
    $$\left(t \wedge \neg x \wedge \neg y\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right)$$ 
    (t∧(¬x)∧(¬y))∨((¬x)∧(¬y)∧(¬z))
    FND [src]
    $$\left(t \wedge \neg x \wedge \neg y\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right)$$ 
    (t∧(¬x)∧(¬y))∨((¬x)∧(¬y)∧(¬z))
    FNCD [src]
    $$\neg x \wedge \neg y \wedge \left(t \vee \neg z\right)$$ 
    (¬x)∧(¬y)∧(t∨(¬z))
    FNC [src]
    Ya está reducido a FNC
    $$\neg x \wedge \neg y \wedge \left(t \vee \neg z\right)$$ 
    (¬x)∧(¬y)∧(t∨(¬z))
    © Sr Examen – Калькулятор