Sr Examen
Lógica matemática/ abc+abd+abe+acd+ace+¬(a+d+e)+¬b¬cd+¬b¬ce+¬(bde)+¬(cde)

Expresión abc+abd+abe+acd+ace+¬(a+d+e)+¬b¬cd+¬b¬ce+¬(bde)+¬(cde)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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