Expresión ¬¬(¬(¬((a∧b)∨(c∧d))∧((c∧d)∨¬b))∨((c∧d)∨¬b))
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$\left(a \wedge b\right) \vee \left(c \wedge d\right) = \left(a \vee c\right) \wedge \left(a \vee d\right) \wedge \left(b \vee c\right) \wedge \left(b \vee d\right)$$
$$\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) = \left(\neg a \wedge \neg c\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
$$\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) \wedge \left(\left(c \wedge d\right) \vee \neg b\right) = \neg b \wedge \left(\neg c \vee \neg d\right)$$
$$\neg \left(\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) \wedge \left(\left(c \wedge d\right) \vee \neg b\right)\right) = b \vee \left(c \wedge d\right)$$
$$\left(c \wedge d\right) \vee \neg b \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) \wedge \left(\left(c \wedge d\right) \vee \neg b\right)\right) = 1$$
$$\neg \left(\left(c \wedge d\right) \vee \neg b \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) \wedge \left(\left(c \wedge d\right) \vee \neg b\right)\right)\right) = \text{False}$$
$$\neg \left(\neg \left(\left(c \wedge d\right) \vee \neg b \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) \wedge \left(\left(c \wedge d\right) \vee \neg b\right)\right)\right)\right) = 1$$
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 | 1 |
+---+---+---+---+--------+
| 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 |
+---+---+---+---+--------+