Sr Examen
Expresión abc+abd+abe+acd+ace+¬(a+d+e)+¬b¬cd+¬b¬ce+¬b¬d¬e+¬b¬d¬e
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)∨(¬(a∨d∨e))∨(d∧(¬b)∧(¬c))∨(e∧(¬b)∧(¬c))∨((¬b)∧(¬d)∧(¬e))
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge d\right) \vee \left(a \wedge b \wedge e\right) \vee \left(a \wedge c \wedge d\right) \vee \left(a \wedge c \wedge e\right) \vee \left(d \wedge \neg b \wedge \neg c\right) \vee \left(e \wedge \neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d \wedge \neg e\right) \vee \neg \left(a \vee d \vee e\right)$$
Solución detallada
$$\neg \left(a \vee d \vee e\right) = \neg a \wedge \neg d \wedge \neg e$$
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge d\right) \vee \left(a \wedge b \wedge e\right) \vee \left(a \wedge c \wedge d\right) \vee \left(a \wedge c \wedge e\right) \vee \left(d \wedge \neg b \wedge \neg c\right) \vee \left(e \wedge \neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d \wedge \neg e\right) \vee \neg \left(a \vee d \vee e\right) = \left(a \wedge c\right) \vee \left(a \wedge d\right) \vee \left(a \wedge e\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg d \wedge \neg e\right)$$
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge d\right) \vee \left(a \wedge b \wedge e\right) \vee \left(a \wedge c \wedge d\right) \vee \left(a \wedge c \wedge e\right) \vee \left(d \wedge \neg b \wedge \neg c\right) \vee \left(e \wedge \neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d \wedge \neg e\right) \vee \neg \left(a \vee d \vee e\right) = \left(a \wedge c\right) \vee \left(a \wedge d\right) \vee \left(a \wedge e\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg d \wedge \neg e\right)$$
Simplificación
[src]
$$\left(a \wedge c\right) \vee \left(a \wedge d\right) \vee \left(a \wedge e\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg d \wedge \neg e\right)$$
(a∧c)∨(a∧d)∨(a∧e)∨((¬b)∧(¬c))∨((¬a)∧(¬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 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 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 | 0 | +---+---+---+---+---+--------+ | 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 | +---+---+---+---+---+--------+
FNCD
[src]
$$\left(a \vee \neg b \vee \neg d\right) \wedge \left(a \vee \neg b \vee \neg e\right) \wedge \left(a \vee \neg c \vee \neg d\right) \wedge \left(a \vee \neg c \vee \neg e\right) \wedge \left(c \vee d \vee e \vee \neg a \vee \neg b\right)$$
(a∨(¬b)∨(¬d))∧(a∨(¬b)∨(¬e))∧(a∨(¬c)∨(¬d))∧(a∨(¬c)∨(¬e))∧(c∨d∨e∨(¬a)∨(¬b))
FND
[src]
Ya está reducido a FND
$$\left(a \wedge c\right) \vee \left(a \wedge d\right) \vee \left(a \wedge e\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg d \wedge \neg e\right)$$
(a∧c)∨(a∧d)∨(a∧e)∨((¬b)∧(¬c))∨((¬a)∧(¬d)∧(¬e))
FNDP
[src]
$$\left(a \wedge c\right) \vee \left(a \wedge d\right) \vee \left(a \wedge e\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg d \wedge \neg e\right)$$
(a∧c)∨(a∧d)∨(a∧e)∨((¬b)∧(¬c))∨((¬a)∧(¬d)∧(¬e))
FNC
[src]
$$\left(a \vee \neg a \vee \neg b\right) \wedge \left(a \vee \neg a \vee \neg c\right) \wedge \left(a \vee \neg b \vee \neg d\right) \wedge \left(a \vee \neg b \vee \neg e\right) \wedge \left(a \vee \neg c \vee \neg d\right) \wedge \left(a \vee \neg c \vee \neg e\right) \wedge \left(a \vee c \vee \neg a \vee \neg b\right) \wedge \left(a \vee c \vee \neg a \vee \neg c\right) \wedge \left(a \vee c \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee \neg b \vee \neg e\right) \wedge \left(a \vee c \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee \neg c \vee \neg e\right) \wedge \left(a \vee d \vee \neg a \vee \neg b\right) \wedge \left(a \vee d \vee \neg a \vee \neg c\right) \wedge \left(a \vee d \vee \neg b \vee \neg d\right) \wedge \left(a \vee d \vee \neg b \vee \neg e\right) \wedge \left(a \vee d \vee \neg c \vee \neg d\right) \wedge \left(a \vee d \vee \neg c \vee \neg e\right) \wedge \left(a \vee e \vee \neg a \vee \neg b\right) \wedge \left(a \vee e \vee \neg a \vee \neg c\right) \wedge \left(a \vee e \vee \neg b \vee \neg d\right) \wedge \left(a \vee e \vee \neg b \vee \neg e\right) \wedge \left(a \vee e \vee \neg c \vee \neg d\right) \wedge \left(a \vee e \vee \neg c \vee \neg e\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg b\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg c\right) \wedge \left(a \vee c \vee d \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg b \vee \neg e\right) \wedge \left(a \vee c \vee d \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg c \vee \neg e\right) \wedge \left(a \vee c \vee e \vee \neg a \vee \neg b\right) \wedge \left(a \vee c \vee e \vee \neg a \vee \neg c\right) \wedge \left(a \vee c \vee e \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee e \vee \neg b \vee \neg e\right) \wedge \left(a \vee c \vee e \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee e \vee \neg c \vee \neg e\right) \wedge \left(a \vee d \vee e \vee \neg a \vee \neg b\right) \wedge \left(a \vee d \vee e \vee \neg a \vee \neg c\right) \wedge \left(a \vee d \vee e \vee \neg b \vee \neg d\right) \wedge \left(a \vee d \vee e \vee \neg b \vee \neg e\right) \wedge \left(a \vee d \vee e \vee \neg c \vee \neg d\right) \wedge \left(a \vee d \vee e \vee \neg c \vee \neg e\right) \wedge \left(c \vee d \vee e \vee \neg a \vee \neg b\right) \wedge \left(c \vee d \vee e \vee \neg a \vee \neg c\right) \wedge \left(c \vee d \vee e \vee \neg b \vee \neg d\right) \wedge \left(c \vee d \vee e \vee \neg b \vee \neg e\right) \wedge \left(c \vee d \vee e \vee \neg c \vee \neg d\right) \wedge \left(c \vee d \vee e \vee \neg c \vee \neg e\right)$$
(a∨(¬a)∨(¬b))∧(a∨(¬a)∨(¬c))∧(a∨(¬b)∨(¬d))∧(a∨(¬b)∨(¬e))∧(a∨(¬c)∨(¬d))∧(a∨(¬c)∨(¬e))∧(a∨c∨(¬a)∨(¬b))∧(a∨c∨(¬a)∨(¬c))∧(a∨c∨(¬b)∨(¬d))∧(a∨c∨(¬b)∨(¬e))∧(a∨c∨(¬c)∨(¬d))∧(a∨c∨(¬c)∨(¬e))∧(a∨d∨(¬a)∨(¬b))∧(a∨d∨(¬a)∨(¬c))∧(a∨d∨(¬b)∨(¬d))∧(a∨d∨(¬b)∨(¬e))∧(a∨d∨(¬c)∨(¬d))∧(a∨d∨(¬c)∨(¬e))∧(a∨e∨(¬a)∨(¬b))∧(a∨e∨(¬a)∨(¬c))∧(a∨e∨(¬b)∨(¬d))∧(a∨e∨(¬b)∨(¬e))∧(a∨e∨(¬c)∨(¬d))∧(a∨e∨(¬c)∨(¬e))∧(a∨c∨d∨(¬a)∨(¬b))∧(a∨c∨d∨(¬a)∨(¬c))∧(a∨c∨d∨(¬b)∨(¬d))∧(a∨c∨d∨(¬b)∨(¬e))∧(a∨c∨d∨(¬c)∨(¬d))∧(a∨c∨d∨(¬c)∨(¬e))∧(a∨c∨e∨(¬a)∨(¬b))∧(a∨c∨e∨(¬a)∨(¬c))∧(a∨c∨e∨(¬b)∨(¬d))∧(a∨c∨e∨(¬b)∨(¬e))∧(a∨c∨e∨(¬c)∨(¬d))∧(a∨c∨e∨(¬c)∨(¬e))∧(a∨d∨e∨(¬a)∨(¬b))∧(a∨d∨e∨(¬a)∨(¬c))∧(a∨d∨e∨(¬b)∨(¬d))∧(a∨d∨e∨(¬b)∨(¬e))∧(a∨d∨e∨(¬c)∨(¬d))∧(a∨d∨e∨(¬c)∨(¬e))∧(c∨d∨e∨(¬a)∨(¬b))∧(c∨d∨e∨(¬a)∨(¬c))∧(c∨d∨e∨(¬b)∨(¬d))∧(c∨d∨e∨(¬b)∨(¬e))∧(c∨d∨e∨(¬c)∨(¬d))∧(c∨d∨e∨(¬c)∨(¬e))