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