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{(x,y)[itex]\in[/itex][itex]ZxZ[/itex]: x+y=10}

Tell me if I'm thinking about this correctly

It is not reflexive because the only 5R5.

It is symmetric because any xRy and yRx where x+y=10.

It is not transitive because any xRy and yRx, x is not related to x.