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