Find Equivalence Classes and the quotient set defined by the relationship in Reals.
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$xTyiff |x^{2}-2|=|y^{2}-2|$ I'd love to solve it but we don't deal in absolutes. Joke aside I have no clue where to start with this one, it has me stumped. If I had been provided the answer to the problem I could just bump around until I got there but its not the case. $x^{2}-y^{2}=0 rightarrow (x+y)(x-y)=0 rightarrow x=y lor x=-y$ Is the only thing that I can scavenge from this, but I doubt it covers all the classes, thus I can't even begin to partition the set. $cl(x)={xin R:x,-x,x-2,2-x}$ But I'm not sure x-2 and 2-x counts in general I think it's only valid if x=0.
discrete-mathematics equivalence-relations set-partition
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