Let R be a relation defined on the set Z of all integers and xRy when x + 2y is divisible by 3. Then
(A) R is not transitive

(B) R is symmetric only
(C) R is an equivalence relation

(D) R is not an equivalence relation

plz explain the answer!!!!

Hi there.. firstly check for reflexive i.e; xRx... In the ques it holds true as 3x is multiple of 3.. to check symmetric say (x,y) is (1,4) as it is true for all (x,y). Check for (y,x) which will be true.. To check transitive let x+2y=3k1 and y+2z=3k2. We need to check whether xRz.. Now add both the above equation we get x+2z+3y=3(k1+k2) or x+2z= 3(k1+k2-y) which is multiple of 3.... Hence it is transitive.. Since all are true it is reflexive.

*at last there should be equivalence instead of reflexive.. I wrote it by mistake.. can you please tell me what you didn`t got it..

Also I think the answer given to the ques is not correct...it is equivalence relation for sure. Can you please tell what did you find wrong in the explanation so I can improve .. For symmetric you can check for any other value too.