Sr Examen
Expresión ¬(¬(a^b)->¬(b^¬c))->¬(¬(c^¬d)->¬(¬c^d))
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(¬((¬(a∧b))⇒(¬(b∧(¬c)))))⇒(¬((¬(c∧(¬d)))⇒(¬(d∧(¬c)))))
$$\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) \Rightarrow \neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(d \wedge \neg c\right)$$
Solución detallada
$$\neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$\neg \left(b \wedge \neg c\right) = c \vee \neg b$$
$$\neg \left(a \wedge b\right) \Rightarrow \neg \left(b \wedge \neg c\right) = a \vee c \vee \neg b$$
$$\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) = b \wedge \neg a \wedge \neg c$$
$$\neg \left(c \wedge \neg d\right) = d \vee \neg c$$
$$\neg \left(d \wedge \neg c\right) = c \vee \neg d$$
$$\neg \left(c \wedge \neg d\right) \Rightarrow \neg \left(d \wedge \neg c\right) = c \vee \neg d$$
$$\neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(d \wedge \neg c\right) = d \wedge \neg c$$
$$\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) \Rightarrow \neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(d \wedge \neg c\right) = a \vee c \vee d \vee \neg b$$
$$\neg \left(b \wedge \neg c\right) = c \vee \neg b$$
$$\neg \left(a \wedge b\right) \Rightarrow \neg \left(b \wedge \neg c\right) = a \vee c \vee \neg b$$
$$\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) = b \wedge \neg a \wedge \neg c$$
$$\neg \left(c \wedge \neg d\right) = d \vee \neg c$$
$$\neg \left(d \wedge \neg c\right) = c \vee \neg d$$
$$\neg \left(c \wedge \neg d\right) \Rightarrow \neg \left(d \wedge \neg c\right) = c \vee \neg d$$
$$\neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(d \wedge \neg c\right) = d \wedge \neg c$$
$$\neg \left(a \wedge b\right) \not\Rightarrow \neg \left(b \wedge \neg c\right) \Rightarrow \neg \left(c \wedge \neg d\right) \not\Rightarrow \neg \left(d \wedge \neg c\right) = a \vee c \vee d \vee \neg b$$
Tabla de verdad
+---+---+---+---+--------+ | a | b | c | d | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+