Sr Examen
Expresión ¬(a^b)*va^(¬b)^cva^b^cv¬(a^b^c)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(a∧b∧c)∨(¬(a∧b))∨(a∧c∧(¬b))∨(¬(a∧b∧c))
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge c \wedge \neg b\right) \vee \neg \left(a \wedge b\right) \vee \neg \left(a \wedge b \wedge c\right)$$
Solución detallada
$$\neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$\neg \left(a \wedge b \wedge c\right) = \neg a \vee \neg b \vee \neg c$$
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge c \wedge \neg b\right) \vee \neg \left(a \wedge b\right) \vee \neg \left(a \wedge b \wedge c\right) = 1$$
$$\neg \left(a \wedge b \wedge c\right) = \neg a \vee \neg b \vee \neg c$$
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge c \wedge \neg b\right) \vee \neg \left(a \wedge b\right) \vee \neg \left(a \wedge b \wedge c\right) = 1$$
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 | +---+---+---+--------+