Expresión abc+abd+abe+acd+ace+¬(a+d+e)+(¬b¬cd)+(¬b¬ce)+(¬b¬d¬e)+(¬b¬d¬e)
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
¬(a∨d∨e)=¬a∧¬d∧¬e(a∧b∧c)∨(a∧b∧d)∨(a∧b∧e)∨(a∧c∧d)∨(a∧c∧e)∨(d∧¬b∧¬c)∨(e∧¬b∧¬c)∨(¬b∧¬d∧¬e)∨¬(a∨d∨e)=(a∧c)∨(a∧d)∨(a∧e)∨(¬b∧¬c)∨(¬a∧¬d∧¬e)
(a∧c)∨(a∧d)∨(a∧e)∨(¬b∧¬c)∨(¬a∧¬d∧¬e)
(a∧c)∨(a∧d)∨(a∧e)∨((¬b)∧(¬c))∨((¬a)∧(¬d)∧(¬e))
Tabla de verdad
+---+---+---+---+---+--------+
| a | b | c | d | e | result |
+===+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0 | 1 |
+---+---+---+---+---+--------+
| 0 | 0 | 0 | 0 | 1 | 1 |
+---+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 0 | 1 |
+---+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1 | 1 |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0 | 1 |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1 | 0 |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 0 | 0 |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1 | 0 |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0 | 1 |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1 | 0 |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0 | 0 |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1 | 0 |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0 | 1 |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1 | 0 |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0 | 0 |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1 | 0 |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0 | 1 |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1 | 1 |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0 | 1 |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1 | 1 |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0 | 1 |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1 | 1 |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0 | 1 |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0 | 0 |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1 | 1 |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0 | 1 |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1 | 1 |
+---+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0 | 1 |
+---+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1 | 1 |
+---+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 0 | 1 |
+---+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+--------+
(a∨¬b∨¬d)∧(a∨¬b∨¬e)∧(a∨¬c∨¬d)∧(a∨¬c∨¬e)∧(c∨d∨e∨¬a∨¬b)
(a∨(¬b)∨(¬d))∧(a∨(¬b)∨(¬e))∧(a∨(¬c)∨(¬d))∧(a∨(¬c)∨(¬e))∧(c∨d∨e∨(¬a)∨(¬b))
Ya está reducido a FND
(a∧c)∨(a∧d)∨(a∧e)∨(¬b∧¬c)∨(¬a∧¬d∧¬e)
(a∧c)∨(a∧d)∨(a∧e)∨((¬b)∧(¬c))∨((¬a)∧(¬d)∧(¬e))
(a∧c)∨(a∧d)∨(a∧e)∨(¬b∧¬c)∨(¬a∧¬d∧¬e)
(a∧c)∨(a∧d)∨(a∧e)∨((¬b)∧(¬c))∨((¬a)∧(¬d)∧(¬e))
(a∨¬a∨¬b)∧(a∨¬a∨¬c)∧(a∨¬b∨¬d)∧(a∨¬b∨¬e)∧(a∨¬c∨¬d)∧(a∨¬c∨¬e)∧(a∨c∨¬a∨¬b)∧(a∨c∨¬a∨¬c)∧(a∨c∨¬b∨¬d)∧(a∨c∨¬b∨¬e)∧(a∨c∨¬c∨¬d)∧(a∨c∨¬c∨¬e)∧(a∨d∨¬a∨¬b)∧(a∨d∨¬a∨¬c)∧(a∨d∨¬b∨¬d)∧(a∨d∨¬b∨¬e)∧(a∨d∨¬c∨¬d)∧(a∨d∨¬c∨¬e)∧(a∨e∨¬a∨¬b)∧(a∨e∨¬a∨¬c)∧(a∨e∨¬b∨¬d)∧(a∨e∨¬b∨¬e)∧(a∨e∨¬c∨¬d)∧(a∨e∨¬c∨¬e)∧(a∨c∨d∨¬a∨¬b)∧(a∨c∨d∨¬a∨¬c)∧(a∨c∨d∨¬b∨¬d)∧(a∨c∨d∨¬b∨¬e)∧(a∨c∨d∨¬c∨¬d)∧(a∨c∨d∨¬c∨¬e)∧(a∨c∨e∨¬a∨¬b)∧(a∨c∨e∨¬a∨¬c)∧(a∨c∨e∨¬b∨¬d)∧(a∨c∨e∨¬b∨¬e)∧(a∨c∨e∨¬c∨¬d)∧(a∨c∨e∨¬c∨¬e)∧(a∨d∨e∨¬a∨¬b)∧(a∨d∨e∨¬a∨¬c)∧(a∨d∨e∨¬b∨¬d)∧(a∨d∨e∨¬b∨¬e)∧(a∨d∨e∨¬c∨¬d)∧(a∨d∨e∨¬c∨¬e)∧(c∨d∨e∨¬a∨¬b)∧(c∨d∨e∨¬a∨¬c)∧(c∨d∨e∨¬b∨¬d)∧(c∨d∨e∨¬b∨¬e)∧(c∨d∨e∨¬c∨¬d)∧(c∨d∨e∨¬c∨¬e)
(a∨(¬a)∨(¬b))∧(a∨(¬a)∨(¬c))∧(a∨(¬b)∨(¬d))∧(a∨(¬b)∨(¬e))∧(a∨(¬c)∨(¬d))∧(a∨(¬c)∨(¬e))∧(a∨c∨(¬a)∨(¬b))∧(a∨c∨(¬a)∨(¬c))∧(a∨c∨(¬b)∨(¬d))∧(a∨c∨(¬b)∨(¬e))∧(a∨c∨(¬c)∨(¬d))∧(a∨c∨(¬c)∨(¬e))∧(a∨d∨(¬a)∨(¬b))∧(a∨d∨(¬a)∨(¬c))∧(a∨d∨(¬b)∨(¬d))∧(a∨d∨(¬b)∨(¬e))∧(a∨d∨(¬c)∨(¬d))∧(a∨d∨(¬c)∨(¬e))∧(a∨e∨(¬a)∨(¬b))∧(a∨e∨(¬a)∨(¬c))∧(a∨e∨(¬b)∨(¬d))∧(a∨e∨(¬b)∨(¬e))∧(a∨e∨(¬c)∨(¬d))∧(a∨e∨(¬c)∨(¬e))∧(a∨c∨d∨(¬a)∨(¬b))∧(a∨c∨d∨(¬a)∨(¬c))∧(a∨c∨d∨(¬b)∨(¬d))∧(a∨c∨d∨(¬b)∨(¬e))∧(a∨c∨d∨(¬c)∨(¬d))∧(a∨c∨d∨(¬c)∨(¬e))∧(a∨c∨e∨(¬a)∨(¬b))∧(a∨c∨e∨(¬a)∨(¬c))∧(a∨c∨e∨(¬b)∨(¬d))∧(a∨c∨e∨(¬b)∨(¬e))∧(a∨c∨e∨(¬c)∨(¬d))∧(a∨c∨e∨(¬c)∨(¬e))∧(a∨d∨e∨(¬a)∨(¬b))∧(a∨d∨e∨(¬a)∨(¬c))∧(a∨d∨e∨(¬b)∨(¬d))∧(a∨d∨e∨(¬b)∨(¬e))∧(a∨d∨e∨(¬c)∨(¬d))∧(a∨d∨e∨(¬c)∨(¬e))∧(c∨d∨e∨(¬a)∨(¬b))∧(c∨d∨e∨(¬a)∨(¬c))∧(c∨d∨e∨(¬b)∨(¬d))∧(c∨d∨e∨(¬b)∨(¬e))∧(c∨d∨e∨(¬c)∨(¬d))∧(c∨d∨e∨(¬c)∨(¬e))