Sr Examen
Lógica matemática/ (A⇔B)∨C

Expresión (A⇔B)∨C

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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