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

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

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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