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