Sr Examen
Lógica matemática/ zxVzcaVcsxVcsa

Expresión zxVzcaVcsxVcsa

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (x∧z)∨(a∧c∧s)∨(a∧c∧z)∨(c∧s∧x)
    $$\left(x \wedge z\right) \vee \left(a \wedge c \wedge s\right) \vee \left(a \wedge c \wedge z\right) \vee \left(c \wedge s \wedge x\right)$$
    Solución detallada
    $$\left(x \wedge z\right) \vee \left(a \wedge c \wedge s\right) \vee \left(a \wedge c \wedge z\right) \vee \left(c \wedge s \wedge x\right) = \left(a \vee x\right) \wedge \left(c \vee x\right) \wedge \left(c \vee z\right) \wedge \left(s \vee z\right)$$
    Simplificación [src]
    $$\left(a \vee x\right) \wedge \left(c \vee x\right) \wedge \left(c \vee z\right) \wedge \left(s \vee z\right)$$ 
    (a∨x)∧(c∨x)∧(c∨z)∧(s∨z)
    Tabla de verdad 
    +---+---+---+---+---+--------+
| a | c | s | x | z | result |
+===+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+---+--------+
| 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      |
+---+---+---+---+---+--------+
    FNC [src]
    Ya está reducido a FNC
    $$\left(a \vee x\right) \wedge \left(c \vee x\right) \wedge \left(c \vee z\right) \wedge \left(s \vee z\right)$$ 
    (a∨x)∧(c∨x)∧(c∨z)∧(s∨z)
    FNDP [src]
    $$\left(x \wedge z\right) \vee \left(a \wedge c \wedge s\right) \vee \left(a \wedge c \wedge z\right) \vee \left(c \wedge s \wedge x\right)$$ 
    (x∧z)∨(a∧c∧s)∨(a∧c∧z)∨(c∧s∧x)
    FND [src]
    $$\left(x \wedge z\right) \vee \left(a \wedge c \wedge s\right) \vee \left(a \wedge c \wedge z\right) \vee \left(a \wedge x \wedge z\right) \vee \left(c \wedge s \wedge x\right) \vee \left(c \wedge x \wedge z\right) \vee \left(s \wedge x \wedge z\right) \vee \left(a \wedge c \wedge s \wedge x\right) \vee \left(a \wedge c \wedge s \wedge z\right) \vee \left(a \wedge c \wedge x \wedge z\right) \vee \left(a \wedge s \wedge x \wedge z\right) \vee \left(c \wedge s \wedge x \wedge z\right)$$ 
    (x∧z)∨(a∧c∧s)∨(a∧c∧z)∨(a∧x∧z)∨(c∧s∧x)∨(c∧x∧z)∨(s∧x∧z)∨(a∧c∧s∧x)∨(a∧c∧s∧z)∨(a∧c∧x∧z)∨(a∧s∧x∧z)∨(c∧s∧x∧z)
    FNCD [src]
    $$\left(a \vee x\right) \wedge \left(c \vee x\right) \wedge \left(c \vee z\right) \wedge \left(s \vee z\right)$$ 
    (a∨x)∧(c∨x)∧(c∨z)∧(s∨z)
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