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Lógica matemática/ a((b⇒c)&(c⇒b))

Expresión a((b⇒c)&(c⇒b))

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    Solución

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