Working out if a given relation is reflexive, symmetric or transitive (or all 3?)

On the set of integers, let 𝑥 be related to 𝑦 precisely when $x\ne y$

On the set of integers, let 𝑥 be related to 𝑦 precisely when $x\ne y$

1. Is this Reflexive?

2. Is this Symmetric?

3. Is this Transitive?

I'm also wondering if it can be multiple? I assume it can maybe be two but maybe not all 3.

To my understanding:

Reflexive is when each element is related to itself, I am not sure how to apply that to $x\ne y$? (Edit: If $x=3$ and $y=3$, then $x\ne y$, so it can't be reflexive as it would be an incorrect statement, so for not equals to it can never be reflexive from what I studied going back over notes)

Symmetric is when x is related to y, it implies that y is related to x (which may be fitting here as x is related to y when they don't equal each other?)

Transitive: When x is related to y, and y is related to z, then x is related to z (Not applicable here? Unsure)

I'm not sure if it's reflex as $x\in Z$ and $y\in Z$ (both are related to the set of integers), it could be symmetric as they are related when $x\ne y$ is the same as being related when $y\ne x$, then I'm not sure of transitive.

On the set of integers, let 𝑥 be related to 𝑦 precisely when $x\ne y$

On the set of integers, let 𝑥 be related to 𝑦 precisely when $x\ne y$

1. Is this Reflexive?

2. Is this Symmetric?

3. Is this Transitive?

I'm also wondering if it can be multiple? I assume it can maybe be two but maybe not all 3.

To my understanding:

Reflexive is when each element is related to itself, I am not sure how to apply that to $x\ne y$? (Edit: If $x=3$ and $y=3$, then $x\ne y$, so it can't be reflexive as it would be an incorrect statement, so for not equals to it can never be reflexive from what I studied going back over notes)

Symmetric is when x is related to y, it implies that y is related to x (which may be fitting here as x is related to y when they don't equal each other?)

Transitive: When x is related to y, and y is related to z, then x is related to z (Not applicable here? Unsure)

I'm not sure if it's reflex as $x\in Z$ and $y\in Z$ (both are related to the set of integers), it could be symmetric as they are related when $x\ne y$ is the same as being related when $y\ne x$, then I'm not sure of transitive.