Expresión bcd+abd+abc+acd
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Solución
Solución detallada
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge d\right) \vee \left(a \wedge c \wedge d\right) \vee \left(b \wedge c \wedge d\right) = \left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(a \vee d\right) \wedge \left(b \vee c\right) \wedge \left(b \vee d\right) \wedge \left(c \vee d\right)$$
$$\left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(a \vee d\right) \wedge \left(b \vee c\right) \wedge \left(b \vee d\right) \wedge \left(c \vee d\right)$$
(a∨b)∧(a∨c)∧(a∨d)∧(b∨c)∧(b∨d)∧(c∨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 | 0 |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0 |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1 |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0 |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0 |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0 |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1 |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0 |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1 |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1 |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+--------+
Ya está reducido a FNC
$$\left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(a \vee d\right) \wedge \left(b \vee c\right) \wedge \left(b \vee d\right) \wedge \left(c \vee d\right)$$
(a∨b)∧(a∨c)∧(a∨d)∧(b∨c)∧(b∨d)∧(c∨d)
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge d\right) \vee \left(a \wedge c \wedge d\right) \vee \left(b \wedge c \wedge d\right)$$
(a∧b∧c)∨(a∧b∧d)∨(a∧c∧d)∨(b∧c∧d)
$$\left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(a \vee d\right) \wedge \left(b \vee c\right) \wedge \left(b \vee d\right) \wedge \left(c \vee d\right)$$
(a∨b)∧(a∨c)∧(a∨d)∧(b∨c)∧(b∨d)∧(c∨d)
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge d\right) \vee \left(a \wedge c \wedge d\right) \vee \left(b \wedge c \wedge d\right) \vee \left(a \wedge b \wedge c \wedge d\right)$$
(a∧b∧c)∨(a∧b∧d)∨(a∧c∧d)∨(b∧c∧d)∨(a∧b∧c∧d)