Sr Examen
Expresión not(not(aandnotb)oraandbandnotc)andnot((aorcorb)andnot(aandnotc))
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬((a∨b∨c)∧(¬(a∧(¬c)))))∧(¬((a∧b∧(¬c))∨(¬(a∧(¬b)))))
$$\neg \left(\neg \left(a \wedge \neg c\right) \wedge \left(a \vee b \vee c\right)\right) \wedge \neg \left(\left(a \wedge b \wedge \neg c\right) \vee \neg \left(a \wedge \neg b\right)\right)$$
Solución detallada
$$\neg \left(a \wedge \neg c\right) = c \vee \neg a$$
$$\neg \left(a \wedge \neg c\right) \wedge \left(a \vee b \vee c\right) = c \vee \left(b \wedge \neg a\right)$$
$$\neg \left(\neg \left(a \wedge \neg c\right) \wedge \left(a \vee b \vee c\right)\right) = \neg c \wedge \left(a \vee \neg b\right)$$
$$\neg \left(a \wedge \neg b\right) = b \vee \neg a$$
$$\left(a \wedge b \wedge \neg c\right) \vee \neg \left(a \wedge \neg b\right) = b \vee \neg a$$
$$\neg \left(\left(a \wedge b \wedge \neg c\right) \vee \neg \left(a \wedge \neg b\right)\right) = a \wedge \neg b$$
$$\neg \left(\neg \left(a \wedge \neg c\right) \wedge \left(a \vee b \vee c\right)\right) \wedge \neg \left(\left(a \wedge b \wedge \neg c\right) \vee \neg \left(a \wedge \neg b\right)\right) = a \wedge \neg b \wedge \neg c$$
$$\neg \left(a \wedge \neg c\right) \wedge \left(a \vee b \vee c\right) = c \vee \left(b \wedge \neg a\right)$$
$$\neg \left(\neg \left(a \wedge \neg c\right) \wedge \left(a \vee b \vee c\right)\right) = \neg c \wedge \left(a \vee \neg b\right)$$
$$\neg \left(a \wedge \neg b\right) = b \vee \neg a$$
$$\left(a \wedge b \wedge \neg c\right) \vee \neg \left(a \wedge \neg b\right) = b \vee \neg a$$
$$\neg \left(\left(a \wedge b \wedge \neg c\right) \vee \neg \left(a \wedge \neg b\right)\right) = a \wedge \neg b$$
$$\neg \left(\neg \left(a \wedge \neg c\right) \wedge \left(a \vee b \vee c\right)\right) \wedge \neg \left(\left(a \wedge b \wedge \neg c\right) \vee \neg \left(a \wedge \neg b\right)\right) = a \wedge \neg b \wedge \neg c$$
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 | +---+---+---+--------+