Sr Examen
Lógica matemática/ ~a*~b*~c+~a*b*c+a*b*~c+a*b*c+

Expresión ~a*~b*~c+~a*b*c+a*b*~c+a*b*c+

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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