Sr Examen
Expresión AB'+A'B'D+A'C'D'
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Solución
Ha introducido
[src]
(¬(a∧b))∨((¬a)∧(¬b)∧(¬c)∧(¬d)∧(¬(a∨d)))
$$\left(\neg a \wedge \neg b \wedge \neg c \wedge \neg d \wedge \neg \left(a \vee d\right)\right) \vee \neg \left(a \wedge b\right)$$
Solución detallada
$$\neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$\neg \left(a \vee d\right) = \neg a \wedge \neg d$$
$$\neg a \wedge \neg b \wedge \neg c \wedge \neg d \wedge \neg \left(a \vee d\right) = \neg a \wedge \neg b \wedge \neg c \wedge \neg d$$
$$\left(\neg a \wedge \neg b \wedge \neg c \wedge \neg d \wedge \neg \left(a \vee d\right)\right) \vee \neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$\neg \left(a \vee d\right) = \neg a \wedge \neg d$$
$$\neg a \wedge \neg b \wedge \neg c \wedge \neg d \wedge \neg \left(a \vee d\right) = \neg a \wedge \neg b \wedge \neg c \wedge \neg d$$
$$\left(\neg a \wedge \neg b \wedge \neg c \wedge \neg d \wedge \neg \left(a \vee d\right)\right) \vee \neg \left(a \wedge b\right) = \neg a \vee \neg b$$
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 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+