Sr Examen
Expresión ¬¬((a+¬b)+a&(b&c))
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Solución
Ha introducido
[src]
¬(¬(a∨(¬b)∨(a∧b∧c)))
$$\neg \left(\neg \left(a \vee \left(a \wedge b \wedge c\right) \vee \neg b\right)\right)$$
Solución detallada
$$a \vee \left(a \wedge b \wedge c\right) \vee \neg b = a \vee \neg b$$
$$\neg \left(a \vee \left(a \wedge b \wedge c\right) \vee \neg b\right) = b \wedge \neg a$$
$$\neg \left(\neg \left(a \vee \left(a \wedge b \wedge c\right) \vee \neg b\right)\right) = a \vee \neg b$$
$$\neg \left(a \vee \left(a \wedge b \wedge c\right) \vee \neg b\right) = b \wedge \neg a$$
$$\neg \left(\neg \left(a \vee \left(a \wedge b \wedge c\right) \vee \neg b\right)\right) = a \vee \neg b$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+