Let R be the relation on the set of real numbers defined by {xRy: x-y is an integer}. Prove that if xRx' and yRy' then (x+y)R(x'+y'). N/B:"R" means "related"

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Well, look at \((x+y)−(x′+y′)=(x−x′)+(y−y′).\) From your assumption, you have that xRx' and yRy'. This means that x−x′ is an integer and y−y′ is an integer. There's basically only one step left. Can you finish it from here?

i was able to come up with that, but i'm still struggling with the finishing

@KingGeorge....must i equate them? if so then m gona gt (x+y)=(x'+y') but duz equality mean "related"

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