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Lógica matemática/ ¬a&¬b&(c&¬d||¬c&d)

Expresión ¬a&¬b&(c&¬d||¬c&d)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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