Sr Examen
Expresión BD+A`C`+ABC+D`C+A`DB+C+ABCD
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
((¬c)∧(¬(a∨(b∧d))))∨((¬(a∨c))∧(¬(d∨(a∧b∧c)))∧(c∨(b∧d)∨(a∧b∧c∧d)))
$$\left(\neg c \wedge \neg \left(a \vee \left(b \wedge d\right)\right)\right) \vee \left(\neg \left(a \vee c\right) \wedge \neg \left(d \vee \left(a \wedge b \wedge c\right)\right) \wedge \left(c \vee \left(b \wedge d\right) \vee \left(a \wedge b \wedge c \wedge d\right)\right)\right)$$
Solución detallada
$$\neg \left(a \vee \left(b \wedge d\right)\right) = \neg a \wedge \left(\neg b \vee \neg d\right)$$
$$\neg c \wedge \neg \left(a \vee \left(b \wedge d\right)\right) = \neg a \wedge \neg c \wedge \left(\neg b \vee \neg d\right)$$
$$\neg \left(a \vee c\right) = \neg a \wedge \neg c$$
$$\neg \left(d \vee \left(a \wedge b \wedge c\right)\right) = \neg d \wedge \left(\neg a \vee \neg b \vee \neg c\right)$$
$$c \vee \left(b \wedge d\right) \vee \left(a \wedge b \wedge c \wedge d\right) = c \vee \left(b \wedge d\right)$$
$$\neg \left(a \vee c\right) \wedge \neg \left(d \vee \left(a \wedge b \wedge c\right)\right) \wedge \left(c \vee \left(b \wedge d\right) \vee \left(a \wedge b \wedge c \wedge d\right)\right) = \text{False}$$
$$\left(\neg c \wedge \neg \left(a \vee \left(b \wedge d\right)\right)\right) \vee \left(\neg \left(a \vee c\right) \wedge \neg \left(d \vee \left(a \wedge b \wedge c\right)\right) \wedge \left(c \vee \left(b \wedge d\right) \vee \left(a \wedge b \wedge c \wedge d\right)\right)\right) = \neg a \wedge \neg c \wedge \left(\neg b \vee \neg d\right)$$
$$\neg c \wedge \neg \left(a \vee \left(b \wedge d\right)\right) = \neg a \wedge \neg c \wedge \left(\neg b \vee \neg d\right)$$
$$\neg \left(a \vee c\right) = \neg a \wedge \neg c$$
$$\neg \left(d \vee \left(a \wedge b \wedge c\right)\right) = \neg d \wedge \left(\neg a \vee \neg b \vee \neg c\right)$$
$$c \vee \left(b \wedge d\right) \vee \left(a \wedge b \wedge c \wedge d\right) = c \vee \left(b \wedge d\right)$$
$$\neg \left(a \vee c\right) \wedge \neg \left(d \vee \left(a \wedge b \wedge c\right)\right) \wedge \left(c \vee \left(b \wedge d\right) \vee \left(a \wedge b \wedge c \wedge d\right)\right) = \text{False}$$
$$\left(\neg c \wedge \neg \left(a \vee \left(b \wedge d\right)\right)\right) \vee \left(\neg \left(a \vee c\right) \wedge \neg \left(d \vee \left(a \wedge b \wedge c\right)\right) \wedge \left(c \vee \left(b \wedge d\right) \vee \left(a \wedge b \wedge c \wedge d\right)\right)\right) = \neg a \wedge \neg c \wedge \left(\neg b \vee \neg d\right)$$
Simplificación
[src]
$$\neg a \wedge \neg c \wedge \left(\neg b \vee \neg d\right)$$
(¬a)∧(¬c)∧((¬b)∨(¬d))
Tabla de verdad
+---+---+---+---+--------+ | a | b | c | d | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+
FND
[src]
$$\left(\neg a \wedge \neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg c \wedge \neg d\right)$$
((¬a)∧(¬b)∧(¬c))∨((¬a)∧(¬c)∧(¬d))
FNDP
[src]
$$\left(\neg a \wedge \neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg c \wedge \neg d\right)$$
((¬a)∧(¬b)∧(¬c))∨((¬a)∧(¬c)∧(¬d))
FNC
[src]
Ya está reducido a FNC
$$\neg a \wedge \neg c \wedge \left(\neg b \vee \neg d\right)$$
(¬a)∧(¬c)∧((¬b)∨(¬d))