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