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