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