Sr Examen

Expresión cv(a⇔b)

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      |
    +---+---+---+--------+
    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))
    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))
    FNDP [src]
    $$c \vee \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
    c∨(a∧b)∨((¬a)∧(¬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))