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Lógica matemática/ ¬[(A^B)v(B^C)v(A^C)v(B^D)]^¬(A^B^C^DvI)

Expresión ¬[(A^B)v(B^C)v(A^C)v(B^D)]^¬(A^B^C^DvI)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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