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Lógica matemática/ （B∧¬H∧¬Z）∨（¬B∧H∧Z）

Expresión （B∧¬H∧¬Z）∨（¬B∧H∧Z）

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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