Expresión ABCD+¬A¬B¬C¬D+¬AB¬CD+A¬BC¬D
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
(a∧b∧c∧d)∨(a∧c∧¬b∧¬d)∨(b∧d∧¬a∧¬c)∨(¬a∧¬b∧¬c∧¬d)=(a∨¬c)∧(b∨¬d)∧(c∨¬a)∧(d∨¬b)
(a∨¬c)∧(b∨¬d)∧(c∨¬a)∧(d∨¬b)
(a∨(¬c))∧(b∨(¬d))∧(c∨(¬a))∧(d∨(¬b))
Tabla de verdad
+---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1 |
+---+---+---+---+--------+
| 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 | 1 |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0 |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0 |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0 |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0 |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+--------+
(a∧b∧c∧d)∨(a∧b∧c∧¬b)∨(a∧b∧d∧¬a)∨(a∧b∧¬a∧¬b)∨(a∧c∧d∧¬d)∨(a∧c∧¬b∧¬d)∨(a∧d∧¬a∧¬d)∨(a∧¬a∧¬b∧¬d)∨(b∧c∧d∧¬c)∨(b∧c∧¬b∧¬c)∨(b∧d∧¬a∧¬c)∨(b∧¬a∧¬b∧¬c)∨(c∧d∧¬c∧¬d)∨(c∧¬b∧¬c∧¬d)∨(d∧¬a∧¬c∧¬d)∨(¬a∧¬b∧¬c∧¬d)
(a∧b∧c∧d)∨(a∧b∧c∧(¬b))∨(a∧b∧d∧(¬a))∨(a∧c∧d∧(¬d))∨(b∧c∧d∧(¬c))∨(a∧b∧(¬a)∧(¬b))∨(a∧c∧(¬b)∧(¬d))∨(a∧d∧(¬a)∧(¬d))∨(b∧c∧(¬b)∧(¬c))∨(b∧d∧(¬a)∧(¬c))∨(c∧d∧(¬c)∧(¬d))∨(a∧(¬a)∧(¬b)∧(¬d))∨(b∧(¬a)∧(¬b)∧(¬c))∨(c∧(¬b)∧(¬c)∧(¬d))∨(d∧(¬a)∧(¬c)∧(¬d))∨((¬a)∧(¬b)∧(¬c)∧(¬d))
Ya está reducido a FNC
(a∨¬c)∧(b∨¬d)∧(c∨¬a)∧(d∨¬b)
(a∨(¬c))∧(b∨(¬d))∧(c∨(¬a))∧(d∨(¬b))
(a∨¬c)∧(b∨¬d)∧(c∨¬a)∧(d∨¬b)
(a∨(¬c))∧(b∨(¬d))∧(c∨(¬a))∧(d∨(¬b))
(a∧b∧c∧d)∨(a∧c∧¬b∧¬d)∨(b∧d∧¬a∧¬c)∨(¬a∧¬b∧¬c∧¬d)
(a∧b∧c∧d)∨(a∧c∧(¬b)∧(¬d))∨(b∧d∧(¬a)∧(¬c))∨((¬a)∧(¬b)∧(¬c)∧(¬d))
