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Lógica matemática/ (!a⇒b*c)+(!(b⇒a*c)⊕b)

Expresión (!a⇒b*c)+(!(b⇒a*c)⊕b)

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    Solución

    Ha introducido [src] 
    ((¬a)⇒(b∧c))∨(b⊕(¬(b⇒(a∧c))))
    $$\left(\neg a \Rightarrow \left(b \wedge c\right)\right) \vee \left(b ⊕ b \not\Rightarrow \left(a \wedge c\right)\right)$$
    Solución detallada
    $$\neg a \Rightarrow \left(b \wedge c\right) = a \vee \left(b \wedge c\right)$$
    $$b \Rightarrow \left(a \wedge c\right) = \left(a \wedge c\right) \vee \neg b$$
    $$b \not\Rightarrow \left(a \wedge c\right) = b \wedge \left(\neg a \vee \neg c\right)$$
    $$b ⊕ b \not\Rightarrow \left(a \wedge c\right) = a \wedge b \wedge c$$
    $$\left(\neg a \Rightarrow \left(b \wedge c\right)\right) \vee \left(b ⊕ b \not\Rightarrow \left(a \wedge c\right)\right) = a \vee \left(b \wedge c\right)$$
    Simplificación [src]
    $$a \vee \left(b \wedge c\right)$$ 
    a∨(b∧c)
    Tabla de verdad 
    +---+---+---+--------+
| a | b | c | result |
+===+===+===+========+
| 0 | 0 | 0 | 0      |
+---+---+---+--------+
| 0 | 0 | 1 | 0      |
+---+---+---+--------+
| 0 | 1 | 0 | 0      |
+---+---+---+--------+
| 0 | 1 | 1 | 1      |
+---+---+---+--------+
| 1 | 0 | 0 | 1      |
+---+---+---+--------+
| 1 | 0 | 1 | 1      |
+---+---+---+--------+
| 1 | 1 | 0 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+
    FND [src]
    Ya está reducido a FND
    $$a \vee \left(b \wedge c\right)$$ 
    a∨(b∧c)
    FNC [src]
    $$\left(a \vee b\right) \wedge \left(a \vee c\right)$$ 
    (a∨b)∧(a∨c)
    FNCD [src]
    $$\left(a \vee b\right) \wedge \left(a \vee c\right)$$ 
    (a∨b)∧(a∨c)
    FNDP [src]
    $$a \vee \left(b \wedge c\right)$$ 
    a∨(b∧c)
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