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

Expresión ¬((¬((¬((a*b)+(c*d)))*(c*d)))*(¬b))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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