So this may be a really simple obvious question, but this is something that kind of trips me up. I'm a beginner at this type of stuff, and still learning.
In my past experience if I see the relation defined, it makes complete sense on how it works, but if a question asks me to find a defined relation I get confused.
Now the question starts with Let R be the relation defined on the set of integer pairs by (x1, y1)R(x2, y2) whenever
$x_{1}^{2}$ + $y_{1}^{2}$ = $x_{2}^{2}$ + $y_{2}^{2}$
What's really throwing me off is the integer pairs.
Now besides this example, a general explanation of defining relations would be nice. Thank you!
Two elements, in this case integer pairs, are related when the sum of the squares of the elements of each pair are equal. To check properties of the relation consider the elements you are already given: $(x_1,y_1)$ and $(x_2,y_2)$. To check if R is reflexive we check if $(x_1,y_1)R(x_1,y_1)$ which is clearly true.