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Lógica matemática/ -(a*b)+a*(-b)*(-d)+a*c*(-d)

Expresión -(a*b)+a*(-b)*(-d)+a*c*(-d)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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