Expresión abc!d+abcd+(a`)b(c`)d+ab(c`)(d`)
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$\left(a \wedge b \wedge c \wedge d\right) \vee \left(a \wedge b \wedge c \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg c \wedge \neg d\right) \vee \left(b \wedge d \wedge \neg a \wedge \neg c\right) = b \wedge \left(a \vee d\right) \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg d\right)$$
$$b \wedge \left(a \vee d\right) \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg d\right)$$
b∧(a∨d)∧(a∨(¬c))∧(c∨(¬a)∨(¬d))
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 | 1 |
+---+---+---+---+--------+
| 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 | 1 |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0 |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1 |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+--------+
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge \neg d\right) \vee \left(b \wedge d \wedge \neg a \wedge \neg c\right)$$
(a∧b∧c)∨(a∧b∧(¬d))∨(b∧d∧(¬a)∧(¬c))
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge \neg a\right) \vee \left(a \wedge b \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge d\right) \vee \left(a \wedge b \wedge c \wedge \neg c\right) \vee \left(a \wedge b \wedge d \wedge \neg a\right) \vee \left(a \wedge b \wedge d \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg a \wedge \neg c\right) \vee \left(a \wedge b \wedge \neg c \wedge \neg d\right) \vee \left(b \wedge c \wedge d \wedge \neg c\right) \vee \left(b \wedge d \wedge \neg a \wedge \neg c\right) \vee \left(b \wedge d \wedge \neg c \wedge \neg d\right)$$
(a∧b∧c)∨(a∧b∧(¬a))∨(a∧b∧(¬d))∨(a∧b∧c∧d)∨(a∧b∧c∧(¬c))∨(a∧b∧d∧(¬a))∨(a∧b∧d∧(¬d))∨(b∧c∧d∧(¬c))∨(a∧b∧(¬a)∧(¬c))∨(a∧b∧(¬c)∧(¬d))∨(b∧d∧(¬a)∧(¬c))∨(b∧d∧(¬c)∧(¬d))
Ya está reducido a FNC
$$b \wedge \left(a \vee d\right) \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg d\right)$$
b∧(a∨d)∧(a∨(¬c))∧(c∨(¬a)∨(¬d))
$$b \wedge \left(a \vee d\right) \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg d\right)$$
b∧(a∨d)∧(a∨(¬c))∧(c∨(¬a)∨(¬d))