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Lógica matemática/ ((¬cvd)&(dva))v((bv¬b)&(¬cv¬a)&(¬cv¬d)&(¬dva))

Expresión ((¬cvd)&(dva))v((bv¬b)&(¬cv¬a)&(¬cv¬d)&(¬dva))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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