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Lógica matemática/ avb⇒¬(bvc)

Expresión avb⇒¬(bvc)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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