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Lógica matemática/ (¬(avb)vc&d)&(¬(dvb)vf)v¬avf

Expresión (¬(avb)vc&d)&(¬(dvb)vf)v¬avf

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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