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