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