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