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