Sr Examen
Lógica matemática/ not(a)*not(b)*not(c)+a*b*not(c)+a*b*c

Expresión not(a)*not(b)*not(c)+a*b*not(c)+a*b*c

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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