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