Sr Examen
Lógica matemática/ ¬(¬((A∨B)∧C))∨¬(¬((a∧b)∨(b∧C)))

Expresión ¬(¬((A∨B)∧C))∨¬(¬((a∧b)∨(b∧C)))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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