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