Sr Examen

  • ¿Cómo usar?

  • Expresión:
  • ~(~(~(~P∧Q)∨~Q)→(~(P∨~Q)))
  • ((a⇒b)⇒(a∨c))⇒((¬b)⇒(¬c))
  • ~((P∧~Q)→P)∨Q
  • !(!(!a*(b⊕c))*!(a*c))

  • Expresiones idénticas

  • (a∨b)∧(a∨c)∧(a∨d)∧(b∨e)∧(c∨d)∧(c∨e)∧(d∨e)∧(a∨(¬e))∧(c∨(¬b))∧(d∨(¬b))∧(e∨(¬a))∧((¬a)∨(¬b))∧((¬b)∨(¬e))∧(b∨(¬c)∨(¬d))∧((¬a)∨(¬c)∨(¬d))∧((¬c)∨(¬¬((a∨b)∧(a∨c))d)∨(¬e))
  • a∨b∧a∨c∧a∨d∧b∨e∧c∨d∧c∨e∧d∨e∧a∨¬e∧c∨¬b∧d∨¬b∧e∨¬a∧¬a∨¬b∧¬b∨¬e∧b∨¬c∨¬d∧¬a∨¬c∨¬d∧¬c∨¬¬a∨b∧a∨cd∨¬e
Lógica matemática/ (a∨b)∧(a∨c)∧(a∨d)∧(b∨e)∧(c∨d)∧(c∨e)∧(d∨e)∧(a∨(¬e))∧(c∨(¬b))∧(d∨(¬b))∧(e∨(¬a))∧((¬a)∨(¬b))∧((¬b)∨(¬e))∧(b∨(¬c)∨(¬d))∧((¬a)∨(¬c)∨(¬d))∧((¬c)∨(¬¬((a∨b)∧(a∨c))d)∨(¬e))

Expresión (a∨b)∧(a∨c)∧(a∨d)∧(b∨e)∧(c∨d)∧(c∨e)∧(d∨e)∧(a∨(¬e))∧(c∨(¬b))∧(d∨(¬b))∧(e∨(¬a))∧((¬a)∨(¬b))∧((¬b)∨(¬e))∧(b∨(¬c)∨(¬d))∧((¬a)∨(¬c)∨(¬d))∧((¬c)∨(¬¬((a∨b)∧(a∨c))d)∨(¬e))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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