Sr Examen
Expresión bac¬d+guke+bake
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⌨
Solución
Ha introducido
[src]
(a∧b∧e∧k)∨(e∧g∧k∧u)∨(a∧b∧c∧(¬d))
$$\left(a \wedge b \wedge c \wedge \neg d\right) \vee \left(a \wedge b \wedge e \wedge k\right) \vee \left(e \wedge g \wedge k \wedge u\right)$$
Solución detallada
$$\left(a \wedge b \wedge c \wedge \neg d\right) \vee \left(a \wedge b \wedge e \wedge k\right) \vee \left(e \wedge g \wedge k \wedge u\right) = \left(a \vee e\right) \wedge \left(a \vee g\right) \wedge \left(a \vee k\right) \wedge \left(a \vee u\right) \wedge \left(b \vee e\right) \wedge \left(b \vee g\right) \wedge \left(b \vee k\right) \wedge \left(b \vee u\right) \wedge \left(c \vee e\right) \wedge \left(c \vee k\right) \wedge \left(e \vee \neg d\right) \wedge \left(k \vee \neg d\right)$$
Simplificación
[src]
$$\left(a \vee e\right) \wedge \left(a \vee g\right) \wedge \left(a \vee k\right) \wedge \left(a \vee u\right) \wedge \left(b \vee e\right) \wedge \left(b \vee g\right) \wedge \left(b \vee k\right) \wedge \left(b \vee u\right) \wedge \left(c \vee e\right) \wedge \left(c \vee k\right) \wedge \left(e \vee \neg d\right) \wedge \left(k \vee \neg d\right)$$
(a∨e)∧(a∨g)∧(a∨k)∧(a∨u)∧(b∨e)∧(b∨g)∧(b∨k)∧(b∨u)∧(c∨e)∧(c∨k)∧(e∨(¬d))∧(k∨(¬d))
Tabla de verdad
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+---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 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+---+---+---+---+---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+---+---+---+---+--------+
FNDP
[src]
$$\left(a \wedge b \wedge c \wedge \neg d\right) \vee \left(a \wedge b \wedge e \wedge k\right) \vee \left(e \wedge g \wedge k \wedge u\right)$$
(a∧b∧e∧k)∨(e∧g∧k∧u)∨(a∧b∧c∧(¬d))
FNC
[src]
Ya está reducido a FNC
$$\left(a \vee e\right) \wedge \left(a \vee g\right) \wedge \left(a \vee k\right) \wedge \left(a \vee u\right) \wedge \left(b \vee e\right) \wedge \left(b \vee g\right) \wedge \left(b \vee k\right) \wedge \left(b \vee u\right) \wedge \left(c \vee e\right) \wedge \left(c \vee k\right) \wedge \left(e \vee \neg d\right) \wedge \left(k \vee \neg d\right)$$
(a∨e)∧(a∨g)∧(a∨k)∧(a∨u)∧(b∨e)∧(b∨g)∧(b∨k)∧(b∨u)∧(c∨e)∧(c∨k)∧(e∨(¬d))∧(k∨(¬d))
FNCD
[src]
$$\left(a \vee e\right) \wedge \left(a \vee g\right) \wedge \left(a \vee k\right) \wedge \left(a \vee u\right) \wedge \left(b \vee e\right) \wedge \left(b \vee g\right) \wedge \left(b \vee k\right) \wedge \left(b \vee u\right) \wedge \left(c \vee e\right) \wedge \left(c \vee k\right) \wedge \left(e \vee \neg d\right) \wedge \left(k \vee \neg d\right)$$
(a∨e)∧(a∨g)∧(a∨k)∧(a∨u)∧(b∨e)∧(b∨g)∧(b∨k)∧(b∨u)∧(c∨e)∧(c∨k)∧(e∨(¬d))∧(k∨(¬d))
FND
[src]
$$\left(a \wedge b \wedge c \wedge \neg d\right) \vee \left(a \wedge b \wedge e \wedge k\right) \vee \left(e \wedge g \wedge k \wedge u\right) \vee \left(a \wedge b \wedge c \wedge e \wedge k\right) \vee \left(a \wedge b \wedge c \wedge e \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge g \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge k \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge e \wedge g \wedge k\right) \vee \left(a \wedge b \wedge e \wedge k \wedge u\right) \vee \left(a \wedge b \wedge e \wedge k \wedge \neg d\right) \vee \left(a \wedge e \wedge g \wedge k \wedge u\right) \vee \left(b \wedge e \wedge g \wedge k \wedge u\right) \vee \left(c \wedge e \wedge g \wedge k \wedge u\right) \vee \left(e \wedge g \wedge k \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge e \wedge g \wedge k\right) \vee \left(a \wedge b \wedge c \wedge e \wedge g \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge e \wedge k \wedge u\right) \vee \left(a \wedge b \wedge c \wedge e \wedge k \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge e \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge g \wedge k \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge g \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge k \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge e \wedge g \wedge k \wedge u\right) \vee \left(a \wedge b \wedge e \wedge g \wedge k \wedge \neg d\right) \vee \left(a \wedge b \wedge e \wedge k \wedge u \wedge \neg d\right) \vee \left(a \wedge c \wedge e \wedge g \wedge k \wedge u\right) \vee \left(a \wedge e \wedge g \wedge k \wedge u \wedge \neg d\right) \vee \left(b \wedge c \wedge e \wedge g \wedge k \wedge u\right) \vee \left(b \wedge e \wedge g \wedge k \wedge u \wedge \neg d\right) \vee \left(c \wedge e \wedge g \wedge k \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge e \wedge g \wedge k \wedge u\right) \vee \left(a \wedge b \wedge c \wedge e \wedge g \wedge k \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge e \wedge g \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge e \wedge k \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge g \wedge k \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge e \wedge g \wedge k \wedge u \wedge \neg d\right) \vee \left(a \wedge c \wedge e \wedge g \wedge k \wedge u \wedge \neg d\right) \vee \left(b \wedge c \wedge e \wedge g \wedge k \wedge u \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge e \wedge g \wedge k \wedge u \wedge \neg d\right)$$
(a∧b∧e∧k)∨(e∧g∧k∧u)∨(a∧b∧c∧(¬d))∨(a∧b∧c∧e∧k)∨(a∧b∧e∧g∧k)∨(a∧b∧e∧k∧u)∨(a∧e∧g∧k∧u)∨(b∧e∧g∧k∧u)∨(c∧e∧g∧k∧u)∨(a∧b∧c∧e∧(¬d))∨(a∧b∧c∧g∧(¬d))∨(a∧b∧c∧k∧(¬d))∨(a∧b∧c∧u∧(¬d))∨(a∧b∧e∧k∧(¬d))∨(e∧g∧k∧u∧(¬d))∨(a∧b∧c∧e∧g∧k)∨(a∧b∧c∧e∧k∧u)∨(a∧b∧e∧g∧k∧u)∨(a∧c∧e∧g∧k∧u)∨(b∧c∧e∧g∧k∧u)∨(a∧b∧c∧e∧g∧(¬d))∨(a∧b∧c∧e∧k∧(¬d))∨(a∧b∧c∧e∧u∧(¬d))∨(a∧b∧c∧g∧k∧(¬d))∨(a∧b∧c∧g∧u∧(¬d))∨(a∧b∧c∧k∧u∧(¬d))∨(a∧b∧e∧g∧k∧(¬d))∨(a∧b∧e∧k∧u∧(¬d))∨(a∧e∧g∧k∧u∧(¬d))∨(b∧e∧g∧k∧u∧(¬d))∨(c∧e∧g∧k∧u∧(¬d))∨(a∧b∧c∧e∧g∧k∧u)∨(a∧b∧c∧e∧g∧k∧(¬d))∨(a∧b∧c∧e∧g∧u∧(¬d))∨(a∧b∧c∧e∧k∧u∧(¬d))∨(a∧b∧c∧g∧k∧u∧(¬d))∨(a∧b∧e∧g∧k∧u∧(¬d))∨(a∧c∧e∧g∧k∧u∧(¬d))∨(b∧c∧e∧g∧k∧u∧(¬d))∨(a∧b∧c∧e∧g∧k∧u∧(¬d))