Sr Examen
Lógica matemática/ d^¬a^(¬b∨c)^(b∨¬c∨¬d∨¬c^¬d)^(a∨¬b∨c)

Expresión d^¬a^(¬b∨c)^(b∨¬c∨¬d∨¬c^¬d)^(a∨¬b∨c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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