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Lógica matemática/ y=(a+b)*(-c)

Expresión y=(a+b)*(-c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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