SOLUTION: Is the following relation (R) symmetric or not? Explain. R={(x,y)∈Z×Z:x^2+y^2=1} where Z is the set of integer numbers.

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Question 1126783: Is the following relation (R) symmetric or not? Explain.
R={(x,y)∈Z×Z:x^2+y^2=1} where Z is the set of integer numbers.
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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This relation is symmetric.


To check it, you should make sure that if (x,y) is the relation, then (y,x) is the relation, too.


In the terms of the given relation, it means to check that 



    if  x^2 + y^2 = 1,  where x and y are integer, then  y and x are integer, too,  and  y^2 + x^2 = 1,



but it is clearly obvious (follows from the commutative property of adding integer numbers).

Answered and proved.


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By the way, the only pairs of this relation are 

    (1,0)
    (-1,0)
    (0,1)
    (0,-1)


Not so many . . . - because your relation is defined over integer numbers . . .