Sr Examen
Expresión (b\cb)ac\(abv(bc\ac))
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(a∧c∧(b|(b∧c)))|((a∧b)∨((b∧c)|(a∧c)))
$$\left(a \wedge c \wedge \left(b | \left(b \wedge c\right)\right)\right) | \left(\left(a \wedge b\right) \vee \left(\left(b \wedge c\right) | \left(a \wedge c\right)\right)\right)$$
Solución detallada
$$b | \left(b \wedge c\right) = \neg b \vee \neg c$$
$$a \wedge c \wedge \left(b | \left(b \wedge c\right)\right) = a \wedge c \wedge \neg b$$
$$\left(b \wedge c\right) | \left(a \wedge c\right) = \neg a \vee \neg b \vee \neg c$$
$$\left(a \wedge b\right) \vee \left(\left(b \wedge c\right) | \left(a \wedge c\right)\right) = 1$$
$$\left(a \wedge c \wedge \left(b | \left(b \wedge c\right)\right)\right) | \left(\left(a \wedge b\right) \vee \left(\left(b \wedge c\right) | \left(a \wedge c\right)\right)\right) = b \vee \neg a \vee \neg c$$
$$a \wedge c \wedge \left(b | \left(b \wedge c\right)\right) = a \wedge c \wedge \neg b$$
$$\left(b \wedge c\right) | \left(a \wedge c\right) = \neg a \vee \neg b \vee \neg c$$
$$\left(a \wedge b\right) \vee \left(\left(b \wedge c\right) | \left(a \wedge c\right)\right) = 1$$
$$\left(a \wedge c \wedge \left(b | \left(b \wedge c\right)\right)\right) | \left(\left(a \wedge b\right) \vee \left(\left(b \wedge c\right) | \left(a \wedge c\right)\right)\right) = b \vee \neg a \vee \neg c$$
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 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+