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Lógica matemática/ abcd∨¬abc¬d

Expresión abcd∨¬abc¬d

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    Solución

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