Sr Examen
Lógica matemática/ (¬(avbvc))v(¬(b))v((¬(av(¬(b))vc))&(¬((¬(a))vbvc)))v(¬(a))&b

Expresión (¬(avbvc))v(¬(b))v((¬(av(¬(b))vc))&(¬((¬(a))vbvc)))v(¬(a))&b

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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