Sr Examen
Lógica matemática/ DA+CDB

Expresión DA+CDB

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    Solución

    Ha introducido [src] 
    (a∧d)∨(b∧c∧d)
    $$\left(a \wedge d\right) \vee \left(b \wedge c \wedge d\right)$$
    Solución detallada
    $$\left(a \wedge d\right) \vee \left(b \wedge c \wedge d\right) = d \wedge \left(a \vee b\right) \wedge \left(a \vee c\right)$$
    Simplificación [src]
    $$d \wedge \left(a \vee b\right) \wedge \left(a \vee c\right)$$ 
    d∧(a∨b)∧(a∨c)
    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 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FND [src]
    $$\left(a \wedge d\right) \vee \left(a \wedge b \wedge d\right) \vee \left(a \wedge c \wedge d\right) \vee \left(b \wedge c \wedge d\right)$$ 
    (a∧d)∨(a∧b∧d)∨(a∧c∧d)∨(b∧c∧d)
    FNCD [src]
    $$d \wedge \left(a \vee b\right) \wedge \left(a \vee c\right)$$ 
    d∧(a∨b)∧(a∨c)
    FNDP [src]
    $$\left(a \wedge d\right) \vee \left(b \wedge c \wedge d\right)$$ 
    (a∧d)∨(b∧c∧d)
    FNC [src]
    Ya está reducido a FNC
    $$d \wedge \left(a \vee b\right) \wedge \left(a \vee c\right)$$ 
    d∧(a∨b)∧(a∨c)
    © Sr Examen – Калькулятор