Sr Examen
Lógica matemática/ AvB⇒C&D

Expresión AvB⇒C&D

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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