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