Sr Examen

Expresión (x∨y)(y→z)(z≡x)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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