Sr Examen
Expresión BDv¬(A¬DvA)(Av¬A¬DVBD)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(b∧d)∨((¬(a∨(a∧(¬d))))∧(a∨(b∧d)∨((¬a)∧(¬d))))
$$\left(b \wedge d\right) \vee \left(\neg \left(a \vee \left(a \wedge \neg d\right)\right) \wedge \left(a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)\right)\right)$$
Solución detallada
$$a \vee \left(a \wedge \neg d\right) = a$$
$$\neg \left(a \vee \left(a \wedge \neg d\right)\right) = \neg a$$
$$a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right) = a \vee b \vee \neg d$$
$$\neg \left(a \vee \left(a \wedge \neg d\right)\right) \wedge \left(a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)\right) = \neg a \wedge \left(b \vee \neg d\right)$$
$$\left(b \wedge d\right) \vee \left(\neg \left(a \vee \left(a \wedge \neg d\right)\right) \wedge \left(a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)\right)\right) = \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)$$
$$\neg \left(a \vee \left(a \wedge \neg d\right)\right) = \neg a$$
$$a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right) = a \vee b \vee \neg d$$
$$\neg \left(a \vee \left(a \wedge \neg d\right)\right) \wedge \left(a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)\right) = \neg a \wedge \left(b \vee \neg d\right)$$
$$\left(b \wedge d\right) \vee \left(\neg \left(a \vee \left(a \wedge \neg d\right)\right) \wedge \left(a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)\right)\right) = \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)$$
Simplificación
[src]
$$\left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)$$
(b∧d)∨((¬a)∧(¬d))
Tabla de verdad
+---+---+---+--------+ | a | b | d | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNC
[src]
$$\left(b \vee \neg a\right) \wedge \left(b \vee \neg d\right) \wedge \left(d \vee \neg a\right) \wedge \left(d \vee \neg d\right)$$
(b∨(¬a))∧(b∨(¬d))∧(d∨(¬a))∧(d∨(¬d))
FND
[src]
Ya está reducido a FND
$$\left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)$$
(b∧d)∨((¬a)∧(¬d))