Expresión BDv¬(A¬DvA)(Av¬A¬DVBD)
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Solución
Solución detallada
$$a \vee \left(a \wedge \neg d\right) = a$$
$$\neg \left(a \vee \left(a \wedge \neg d\right)\right) = \neg a$$
$$a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right) = a \vee b \vee \neg d$$
$$\neg \left(a \vee \left(a \wedge \neg d\right)\right) \wedge \left(a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)\right) = \neg a \wedge \left(b \vee \neg d\right)$$
$$\left(b \wedge d\right) \vee \left(\neg \left(a \vee \left(a \wedge \neg d\right)\right) \wedge \left(a \vee \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)\right)\right) = \left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)$$
$$\left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)$$
Tabla de verdad
+---+---+---+--------+
| a | b | d | result |
+===+===+===+========+
| 0 | 0 | 0 | 1 |
+---+---+---+--------+
| 0 | 0 | 1 | 0 |
+---+---+---+--------+
| 0 | 1 | 0 | 1 |
+---+---+---+--------+
| 0 | 1 | 1 | 1 |
+---+---+---+--------+
| 1 | 0 | 0 | 0 |
+---+---+---+--------+
| 1 | 0 | 1 | 0 |
+---+---+---+--------+
| 1 | 1 | 0 | 0 |
+---+---+---+--------+
| 1 | 1 | 1 | 1 |
+---+---+---+--------+
$$\left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)$$
$$\left(b \vee \neg a\right) \wedge \left(b \vee \neg d\right) \wedge \left(d \vee \neg a\right) \wedge \left(d \vee \neg d\right)$$
(b∨(¬a))∧(b∨(¬d))∧(d∨(¬a))∧(d∨(¬d))
$$\left(b \vee \neg d\right) \wedge \left(d \vee \neg a\right)$$
Ya está reducido a FND
$$\left(b \wedge d\right) \vee \left(\neg a \wedge \neg d\right)$$