Prove that the relation is an equivalence relation. The relation T on RxR given by (x,y)T(a,b) iff x^2+y^2=a^2+b^2. Sketch the equivalence class of (1,2)

Question

Prove that the relation is an equivalence relation. The relation T on RxR given by (x,y)T(a,b) iff x^2+y^2=a^2+b^2.  Sketch the equivalence class of (1,2)

akashdeepdeb · Answer

Can you prove Reflexivity?

anonymous · Answer

I'm not sure how to even begin this.

ikram002p · Answer

i think   u have to show that   T is equivalence relation mm
    1- the reflexive law holds .
    2- the symmetric law holds .
   3- the transitive law holds .

ikram002p · Answer

and as i see
for this 
  (x,y)T(a,b) iff x^2+y^2=a^2+b^2.
its a circl 
x^2+y^2=r^2=a^2+b^2.
so for (1,2)
its a circle with radues $\sqrt 5$ center 0,0
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