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