Sr Examen
Expresión ¬(¬a&b&¬c)⇒¬(av¬bvc)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬(b∧(¬a)∧(¬c)))⇒(¬(a∨c∨(¬b)))
$$\neg \left(b \wedge \neg a \wedge \neg c\right) \Rightarrow \neg \left(a \vee c \vee \neg b\right)$$
Solución detallada
$$\neg \left(b \wedge \neg a \wedge \neg c\right) = a \vee c \vee \neg b$$
$$\neg \left(a \vee c \vee \neg b\right) = b \wedge \neg a \wedge \neg c$$
$$\neg \left(b \wedge \neg a \wedge \neg c\right) \Rightarrow \neg \left(a \vee c \vee \neg b\right) = b \wedge \neg a \wedge \neg c$$
$$\neg \left(a \vee c \vee \neg b\right) = b \wedge \neg a \wedge \neg c$$
$$\neg \left(b \wedge \neg a \wedge \neg c\right) \Rightarrow \neg \left(a \vee c \vee \neg b\right) = b \wedge \neg a \wedge \neg c$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+