Sr Examen
Lógica matemática/ ¬(¬a∨b&с)&(a&¬bvc)&(¬(av¬b)vc)v¬(avb&c)

Expresión ¬(¬a∨b&с)&(a&¬bvc)&(¬(av¬b)vc)v¬(avb&c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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