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Lógica matemática/ abc(d`)+abcd+(a`)b(c`)d+ab(cd`)

Expresión abc(d`)+abcd+(a`)b(c`)d+ab(cd`)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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