Sr Examen
Expresión ¬(¬(AvB)&C)v¬((¬B⇒C)vD)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬(c∧(¬(a∨b))))∨(¬(d∨((¬b)⇒c)))
$$\neg \left(c \wedge \neg \left(a \vee b\right)\right) \vee \neg \left(d \vee \left(\neg b \Rightarrow c\right)\right)$$
Solución detallada
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$c \wedge \neg \left(a \vee b\right) = c \wedge \neg a \wedge \neg b$$
$$\neg \left(c \wedge \neg \left(a \vee b\right)\right) = a \vee b \vee \neg c$$
$$\neg b \Rightarrow c = b \vee c$$
$$d \vee \left(\neg b \Rightarrow c\right) = b \vee c \vee d$$
$$\neg \left(d \vee \left(\neg b \Rightarrow c\right)\right) = \neg b \wedge \neg c \wedge \neg d$$
$$\neg \left(c \wedge \neg \left(a \vee b\right)\right) \vee \neg \left(d \vee \left(\neg b \Rightarrow c\right)\right) = a \vee b \vee \neg c$$
$$c \wedge \neg \left(a \vee b\right) = c \wedge \neg a \wedge \neg b$$
$$\neg \left(c \wedge \neg \left(a \vee b\right)\right) = a \vee b \vee \neg c$$
$$\neg b \Rightarrow c = b \vee c$$
$$d \vee \left(\neg b \Rightarrow c\right) = b \vee c \vee d$$
$$\neg \left(d \vee \left(\neg b \Rightarrow c\right)\right) = \neg b \wedge \neg c \wedge \neg d$$
$$\neg \left(c \wedge \neg \left(a \vee b\right)\right) \vee \neg \left(d \vee \left(\neg b \Rightarrow c\right)\right) = a \vee b \vee \neg c$$
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 | 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 | +---+---+---+---+--------+