Sr Examen
Expresión ¬((¬((¬((a*b)+(c*d)))*(c*d)))*(¬b))
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
¬((¬b)∧(¬(c∧d∧(¬((a∧b)∨(c∧d))))))
$$\neg \left(\neg b \wedge \neg \left(c \wedge d \wedge \neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right)\right)\right)$$
Solución detallada
$$\left(a \wedge b\right) \vee \left(c \wedge d\right) = \left(a \vee c\right) \wedge \left(a \vee d\right) \wedge \left(b \vee c\right) \wedge \left(b \vee d\right)$$
$$\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) = \left(\neg a \wedge \neg c\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
$$c \wedge d \wedge \neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) = \text{False}$$
$$\neg \left(c \wedge d \wedge \neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right)\right) = 1$$
$$\neg b \wedge \neg \left(c \wedge d \wedge \neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right)\right) = \neg b$$
$$\neg \left(\neg b \wedge \neg \left(c \wedge d \wedge \neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right)\right)\right) = b$$
$$\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) = \left(\neg a \wedge \neg c\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
$$c \wedge d \wedge \neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) = \text{False}$$
$$\neg \left(c \wedge d \wedge \neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right)\right) = 1$$
$$\neg b \wedge \neg \left(c \wedge d \wedge \neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right)\right) = \neg b$$
$$\neg \left(\neg b \wedge \neg \left(c \wedge d \wedge \neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right)\right)\right) = b$$
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 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+