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Lógica matemática/ М&b&(b&cvc)va&c(a&b)

Expresión М&b&(b&cvc)va&c(a&b)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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