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## Main Question or Discussion Point

Is the set of all integers where <x,y> [itex]\in[/itex]

*R*if and only if (y = x + 3) & (y = x – 3) an empty set?- Thread starter Bob4040
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- #1

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Is the set of all integers where <x,y> [itex]\in[/itex] *R* if and only if (y = x + 3) & (y = x – 3) an empty set?

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chiro

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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?

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chiro

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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.

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Thank you for the help!

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Bacle2

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identity would hold if x were in the set called Z_3, where 3=-3 :

http://www.wolframalpha.com/input/?i=Z+mod+3

Then,for all x, x+3=x-3 .

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