Sr Examen
Lógica matemática/ F=A*B+A*C+B*C

Expresión F=A*B+A*C+B*C

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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