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Lógica matemática/ F=¬(A&B&C)v(B&Cv¬A)

Expresión F=¬(A&B&C)v(B&Cv¬A)

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    Solución

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