Sr Examen
Lógica matemática/ (¬abc)∨(abc)∨(bc)∨(a¬b¬c)

Expresión (¬abc)∨(abc)∨(bc)∨(a¬b¬c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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