Expresión ab∨ac∨bc∨abc∨¬a¬b¬c
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
(a∧b)∨(a∧c)∨(b∧c)∨(a∧b∧c)∨(¬a∧¬b∧¬c)=(a∧b)∨(a∧c)∨(b∧c)∨(¬a∧¬b∧¬c)
(a∧b)∨(a∧c)∨(b∧c)∨(¬a∧¬b∧¬c)
(a∧b)∨(a∧c)∨(b∧c)∨((¬a)∧(¬b)∧(¬c))
Tabla de verdad
+---+---+---+--------+
| a | b | c | result |
+===+===+===+========+
| 0 | 0 | 0 | 1 |
+---+---+---+--------+
| 0 | 0 | 1 | 0 |
+---+---+---+--------+
| 0 | 1 | 0 | 0 |
+---+---+---+--------+
| 0 | 1 | 1 | 1 |
+---+---+---+--------+
| 1 | 0 | 0 | 0 |
+---+---+---+--------+
| 1 | 0 | 1 | 1 |
+---+---+---+--------+
| 1 | 1 | 0 | 1 |
+---+---+---+--------+
| 1 | 1 | 1 | 1 |
+---+---+---+--------+
(a∧b)∨(a∧c)∨(b∧c)∨(¬a∧¬b∧¬c)
(a∧b)∨(a∧c)∨(b∧c)∨((¬a)∧(¬b)∧(¬c))
(a∨b∨¬a)∧(a∨b∨¬b)∧(a∨b∨¬c)∧(a∨c∨¬a)∧(a∨c∨¬b)∧(a∨c∨¬c)∧(b∨c∨¬a)∧(b∨c∨¬b)∧(b∨c∨¬c)∧(a∨b∨c∨¬a)∧(a∨b∨c∨¬b)∧(a∨b∨c∨¬c)
(a∨b∨(¬a))∧(a∨b∨(¬b))∧(a∨b∨(¬c))∧(a∨c∨(¬a))∧(a∨c∨(¬b))∧(a∨c∨(¬c))∧(b∨c∨(¬a))∧(b∨c∨(¬b))∧(b∨c∨(¬c))∧(a∨b∨c∨(¬a))∧(a∨b∨c∨(¬b))∧(a∨b∨c∨(¬c))
(a∨b∨¬c)∧(a∨c∨¬b)∧(b∨c∨¬a)
(a∨b∨(¬c))∧(a∨c∨(¬b))∧(b∨c∨(¬a))
Ya está reducido a FND
(a∧b)∨(a∧c)∨(b∧c)∨(¬a∧¬b∧¬c)
(a∧b)∨(a∧c)∨(b∧c)∨((¬a)∧(¬b)∧(¬c))
