Sr Examen
Lógica matemática/ (B&¬A&B)v(B&¬B&C)v(B&¬B&A)v(B&¬C&C)v(B&¬C&A)v(C&¬A&B)v(C&¬B&C)v(C&¬B&A)v(C&¬C&C)v(C&¬C&A)

Expresión (B&¬A&B)v(B&¬B&C)v(B&¬B&A)v(B&¬C&C)v(B&¬C&A)v(C&¬A&B)v(C&¬B&C)v(C&¬B&A)v(C&¬C&C)v(C&¬C&A)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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