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Lógica matemática/ AC(¬A¬B+C)+¬A¬C(¬A+¬¬BC)

Expresión AC(¬A¬B+C)+¬A¬C(¬A+¬¬BC)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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