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Expresión ¬(¬(a^b)->¬(b^¬c))->¬(¬(c^¬d)->¬(¬b^c))->¬(¬c^d)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
((¬((¬(a∧b))⇒(¬(b∧(¬c)))))⇒(¬((¬(c∧(¬d)))⇒(¬(c∧(¬b))))))⇒(¬(d∧(¬c)))
$$\left(\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) \Rightarrow \neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(c \wedge \neg b\right)\right) \Rightarrow \neg \left(d \wedge \neg c\right)$$
Solución detallada
$$\neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$\neg \left(b \wedge \neg c\right) = c \vee \neg b$$
$$\neg \left(a \wedge b\right) \Rightarrow \neg \left(b \wedge \neg c\right) = a \vee c \vee \neg b$$
$$\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) = b \wedge \neg a \wedge \neg c$$
$$\neg \left(c \wedge \neg d\right) = d \vee \neg c$$
$$\neg \left(c \wedge \neg b\right) = b \vee \neg c$$
$$\neg \left(c \wedge \neg d\right) \Rightarrow \neg \left(c \wedge \neg b\right) = b \vee \neg c \vee \neg d$$
$$\neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(c \wedge \neg b\right) = c \wedge d \wedge \neg b$$
$$\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) \Rightarrow \neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(c \wedge \neg b\right) = a \vee c \vee \neg b$$
$$\neg \left(d \wedge \neg c\right) = c \vee \neg d$$
$$\left(\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) \Rightarrow \neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(c \wedge \neg b\right)\right) \Rightarrow \neg \left(d \wedge \neg c\right) = c \vee \left(b \wedge \neg a\right) \vee \neg d$$
$$\neg \left(b \wedge \neg c\right) = c \vee \neg b$$
$$\neg \left(a \wedge b\right) \Rightarrow \neg \left(b \wedge \neg c\right) = a \vee c \vee \neg b$$
$$\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) = b \wedge \neg a \wedge \neg c$$
$$\neg \left(c \wedge \neg d\right) = d \vee \neg c$$
$$\neg \left(c \wedge \neg b\right) = b \vee \neg c$$
$$\neg \left(c \wedge \neg d\right) \Rightarrow \neg \left(c \wedge \neg b\right) = b \vee \neg c \vee \neg d$$
$$\neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(c \wedge \neg b\right) = c \wedge d \wedge \neg b$$
$$\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) \Rightarrow \neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(c \wedge \neg b\right) = a \vee c \vee \neg b$$
$$\neg \left(d \wedge \neg c\right) = c \vee \neg d$$
$$\left(\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) \Rightarrow \neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(c \wedge \neg b\right)\right) \Rightarrow \neg \left(d \wedge \neg c\right) = c \vee \left(b \wedge \neg a\right) \vee \neg d$$
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 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+
FNCD
[src]
$$\left(b \vee c \vee \neg d\right) \wedge \left(c \vee \neg a \vee \neg d\right)$$
(b∨c∨(¬d))∧(c∨(¬a)∨(¬d))
FNC
[src]
$$\left(b \vee c \vee \neg d\right) \wedge \left(c \vee \neg a \vee \neg d\right)$$
(b∨c∨(¬d))∧(c∨(¬a)∨(¬d))
FND
[src]
Ya está reducido a FND
$$c \vee \left(b \wedge \neg a\right) \vee \neg d$$
c∨(¬d)∨(b∧(¬a))