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Lógica matemática/ ((¬bv¬c)&(avb))v(d&¬c)v(((¬b&¬a)vc)&(avb))

Expresión ((¬bv¬c)&(avb))v(d&¬c)v(((¬b&¬a)vc)&(avb))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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