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Lógica matemática/ ABC+AB'C+AB'C'+A'BC+A'B'C'

Expresión ABC+AB'C+AB'C'+A'BC+A'B'C'

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    Solución

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