Sr Examen
Expresión av(b&c&(avc))=(avb)&(avc)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
((a∨b)∧(a∨c))⇔(a∨(b∧c∧(a∨c)))
$$\left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) ⇔ \left(a \vee \left(b \wedge c \wedge \left(a \vee c\right)\right)\right)$$
Solución detallada
$$\left(a \vee b\right) \wedge \left(a \vee c\right) = a \vee \left(b \wedge c\right)$$
$$b \wedge c \wedge \left(a \vee c\right) = b \wedge c$$
$$a \vee \left(b \wedge c \wedge \left(a \vee c\right)\right) = a \vee \left(b \wedge c\right)$$
$$\left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) ⇔ \left(a \vee \left(b \wedge c \wedge \left(a \vee c\right)\right)\right) = 1$$
$$b \wedge c \wedge \left(a \vee c\right) = b \wedge c$$
$$a \vee \left(b \wedge c \wedge \left(a \vee c\right)\right) = a \vee \left(b \wedge c\right)$$
$$\left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) ⇔ \left(a \vee \left(b \wedge c \wedge \left(a \vee c\right)\right)\right) = 1$$
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 | +---+---+---+--------+