Your definition is a little vague. You mention integers but then you say x and y are real numbers which is a bit of a contradiction.
Are you trying to ask whether x and y are real numbers if the relation holds?
#3
Bob4040
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I do not mean all real numbers. R is the set. x and y are members of the set on the condition that (y = x + 3) & (y = x – 3). These two lines never intersect, so I think that means it is an empty set?
Well the easiest way to check is to set them equal to one another and see if you get a solution or a contradiction.
y = x + 3, y = x - 3 implies x + 3 = x - 3 which implies 3 = -3 which is a contradiction, so you have proven that no element exists satisfying the relationship so you have the empty set.