Sr Examen
Lógica matemática/ ¬((a*b)+(c*d))

Expresión ¬((a*b)+(c*d))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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