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Lógica matemática/ F1=¬(a&b)∨¬(b∨c)

Expresión F1=¬(a&b)∨¬(b∨c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    f1⇔((¬(a∧b))∨(¬(b∨c)))
    $$f_{1} ⇔ \left(\neg \left(a \wedge b\right) \vee \neg \left(b \vee c\right)\right)$$
    Solución detallada
    $$\neg \left(a \wedge b\right) = \neg a \vee \neg b$$
    $$\neg \left(b \vee c\right) = \neg b \wedge \neg c$$
    $$\neg \left(a \wedge b\right) \vee \neg \left(b \vee c\right) = \neg a \vee \neg b$$
    $$f_{1} ⇔ \left(\neg \left(a \wedge b\right) \vee \neg \left(b \vee c\right)\right) = \left(f_{1} \wedge \neg a\right) \vee \left(f_{1} \wedge \neg b\right) \vee \left(a \wedge b \wedge \neg f_{1}\right)$$
    Simplificación [src]
    $$\left(f_{1} \wedge \neg a\right) \vee \left(f_{1} \wedge \neg b\right) \vee \left(a \wedge b \wedge \neg f_{1}\right)$$ 
    (f1∧(¬a))∨(f1∧(¬b))∨(a∧b∧(¬f1))
    Tabla de verdad 
    +---+---+---+----+--------+
| a | b | c | f1 | result |
+===+===+===+====+========+
| 0 | 0 | 0 | 0  | 0      |
+---+---+---+----+--------+
| 0 | 0 | 0 | 1  | 1      |
+---+---+---+----+--------+
| 0 | 0 | 1 | 0  | 0      |
+---+---+---+----+--------+
| 0 | 0 | 1 | 1  | 1      |
+---+---+---+----+--------+
| 0 | 1 | 0 | 0  | 0      |
+---+---+---+----+--------+
| 0 | 1 | 0 | 1  | 1      |
+---+---+---+----+--------+
| 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  | 1      |
+---+---+---+----+--------+
| 1 | 1 | 0 | 1  | 0      |
+---+---+---+----+--------+
| 1 | 1 | 1 | 0  | 1      |
+---+---+---+----+--------+
| 1 | 1 | 1 | 1  | 0      |
+---+---+---+----+--------+
    FNDP [src]
    $$\left(f_{1} \wedge \neg a\right) \vee \left(f_{1} \wedge \neg b\right) \vee \left(a \wedge b \wedge \neg f_{1}\right)$$ 
    (f1∧(¬a))∨(f1∧(¬b))∨(a∧b∧(¬f1))
    FNC [src]
    $$\left(a \vee f_{1}\right) \wedge \left(b \vee f_{1}\right) \wedge \left(f_{1} \vee \neg f_{1}\right) \wedge \left(a \vee f_{1} \vee \neg a\right) \wedge \left(a \vee f_{1} \vee \neg b\right) \wedge \left(a \vee \neg a \vee \neg b\right) \wedge \left(b \vee f_{1} \vee \neg a\right) \wedge \left(b \vee f_{1} \vee \neg b\right) \wedge \left(b \vee \neg a \vee \neg b\right) \wedge \left(f_{1} \vee \neg a \vee \neg f_{1}\right) \wedge \left(f_{1} \vee \neg b \vee \neg f_{1}\right) \wedge \left(\neg a \vee \neg b \vee \neg f_{1}\right)$$ 
    (a∨f1)∧(b∨f1)∧(f1∨(¬f1))∧(a∨f1∨(¬a))∧(a∨f1∨(¬b))∧(b∨f1∨(¬a))∧(b∨f1∨(¬b))∧(a∨(¬a)∨(¬b))∧(b∨(¬a)∨(¬b))∧(f1∨(¬a)∨(¬f1))∧(f1∨(¬b)∨(¬f1))∧((¬a)∨(¬b)∨(¬f1))
    FND [src]
    Ya está reducido a FND
    $$\left(f_{1} \wedge \neg a\right) \vee \left(f_{1} \wedge \neg b\right) \vee \left(a \wedge b \wedge \neg f_{1}\right)$$ 
    (f1∧(¬a))∨(f1∧(¬b))∨(a∧b∧(¬f1))
    FNCD [src]
    $$\left(a \vee f_{1}\right) \wedge \left(b \vee f_{1}\right) \wedge \left(\neg a \vee \neg b \vee \neg f_{1}\right)$$ 
    (a∨f1)∧(b∨f1)∧((¬a)∨(¬b)∨(¬f1))
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