Question

Consider the divisibility relation on the set S = {-5,-3,-2,2,3,5}

To be more precise, this is the relation:
R = {(x, y) ∈ S^2| x divides y}.

Is the relation Reflexive? Symmetric? Anti-symmetric? Transitive?

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The relation is reflexive because all inputs of x is related to itself.

The relation is not symmetric because x/y =/= y/x

Would it be anti-symmetric?

For transitive, I understand that if xRy, yRz, then xRz, but what would the z values be?

Also, what are the x and y values for this? Or is it for any values of x and y? I don't get where the x and y inputs come from. Would the x and y values be one of the values from {-5,-3,-2,2,3,5}?