Sr Examen
Expresión a&!b&!cv!(b&c)v!(a&d)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬(a∧d))∨(¬(b∧c))∨(a∧(¬b)∧(¬c))
$$\left(a \wedge \neg b \wedge \neg c\right) \vee \neg \left(a \wedge d\right) \vee \neg \left(b \wedge c\right)$$
Solución detallada
$$\neg \left(a \wedge d\right) = \neg a \vee \neg d$$
$$\neg \left(b \wedge c\right) = \neg b \vee \neg c$$
$$\left(a \wedge \neg b \wedge \neg c\right) \vee \neg \left(a \wedge d\right) \vee \neg \left(b \wedge c\right) = \neg a \vee \neg b \vee \neg c \vee \neg d$$
$$\neg \left(b \wedge c\right) = \neg b \vee \neg c$$
$$\left(a \wedge \neg b \wedge \neg c\right) \vee \neg \left(a \wedge d\right) \vee \neg \left(b \wedge c\right) = \neg a \vee \neg b \vee \neg c \vee \neg d$$
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 | 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 | 0 | +---+---+---+---+--------+