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Lógica matemática/ BD+BA+A~C+BC

Expresión BD+BA+A~C+BC

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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