Sr Examen
Expresión ¬(A→(B∧C)→D)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
¬((a⇒(b∧c))⇒d)
$$\left(a \Rightarrow \left(b \wedge c\right)\right) \not\Rightarrow d$$
Solución detallada
$$a \Rightarrow \left(b \wedge c\right) = \left(b \wedge c\right) \vee \neg a$$
$$\left(a \Rightarrow \left(b \wedge c\right)\right) \Rightarrow d = d \vee \left(a \wedge \neg b\right) \vee \left(a \wedge \neg c\right)$$
$$\left(a \Rightarrow \left(b \wedge c\right)\right) \not\Rightarrow d = \neg d \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg a\right)$$
$$\left(a \Rightarrow \left(b \wedge c\right)\right) \Rightarrow d = d \vee \left(a \wedge \neg b\right) \vee \left(a \wedge \neg c\right)$$
$$\left(a \Rightarrow \left(b \wedge c\right)\right) \not\Rightarrow d = \neg d \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg a\right)$$
Simplificación
[src]
$$\neg d \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg a\right)$$
(¬d)∧(b∨(¬a))∧(c∨(¬a))
Tabla de verdad
+---+---+---+---+--------+ | a | b | c | d | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 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 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+
FNC
[src]
Ya está reducido a FNC
$$\neg d \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg a\right)$$
(¬d)∧(b∨(¬a))∧(c∨(¬a))
FNDP
[src]
$$\left(\neg a \wedge \neg d\right) \vee \left(b \wedge c \wedge \neg d\right)$$
((¬a)∧(¬d))∨(b∧c∧(¬d))
FND
[src]
$$\left(\neg a \wedge \neg d\right) \vee \left(b \wedge c \wedge \neg d\right) \vee \left(b \wedge \neg a \wedge \neg d\right) \vee \left(c \wedge \neg a \wedge \neg d\right)$$
((¬a)∧(¬d))∨(b∧c∧(¬d))∨(b∧(¬a)∧(¬d))∨(c∧(¬a)∧(¬d))
FNCD
[src]
$$\neg d \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg a\right)$$
(¬d)∧(b∨(¬a))∧(c∨(¬a))