Sr Examen
Expresión ¬¬(a∨b)=>¬(b∨c)
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Solución
Ha introducido
[src]
¬((¬(a∨b))⇒(¬(b∨c)))
$$\neg \left(a \vee b\right) \not\Rightarrow \neg \left(b \vee c\right)$$
Solución detallada
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$\neg \left(b \vee c\right) = \neg b \wedge \neg c$$
$$\neg \left(a \vee b\right) \Rightarrow \neg \left(b \vee c\right) = a \vee b \vee \neg c$$
$$\neg \left(a \vee b\right) \not\Rightarrow \neg \left(b \vee c\right) = c \wedge \neg a \wedge \neg b$$
$$\neg \left(b \vee c\right) = \neg b \wedge \neg c$$
$$\neg \left(a \vee b\right) \Rightarrow \neg \left(b \vee c\right) = a \vee b \vee \neg c$$
$$\neg \left(a \vee b\right) \not\Rightarrow \neg \left(b \vee c\right) = c \wedge \neg a \wedge \neg b$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+