Sr Examen
Expresión not(not(a)*b+a*not(b)+not(a*b)+c)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
¬(c∨(a∧(¬b))∨(b∧(¬a))∨(¬(a∧b)))
$$\neg \left(c \vee \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right) \vee \neg \left(a \wedge b\right)\right)$$
Solución detallada
$$\neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$c \vee \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right) \vee \neg \left(a \wedge b\right) = c \vee \neg a \vee \neg b$$
$$\neg \left(c \vee \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right) \vee \neg \left(a \wedge b\right)\right) = a \wedge b \wedge \neg c$$
$$c \vee \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right) \vee \neg \left(a \wedge b\right) = c \vee \neg a \vee \neg b$$
$$\neg \left(c \vee \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right) \vee \neg \left(a \wedge b\right)\right) = a \wedge b \wedge \neg c$$
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 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+