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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!!!!

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!!!!

Grade:12th pass

6 Answers

Amit
405 Points
5 years ago
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.
sohan goswami
23 Points
5 years ago
hello , but the answer provided is not equivalence , but after providing each and every reason u said at the last the answer is reflexive. But how? i didn't get that!!!!
Amit
405 Points
5 years ago
*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..
Amit
405 Points
5 years ago
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.
sohan goswami
23 Points
5 years ago
yes i am also getting equivalence relation but the question is of wbjee 2016 maths paper , so the solution is given of not an equivalence relation
Ishita
13 Points
2 years ago
The equations are not symmetric for x,y as 2,1
x+2y=3k is multiple of 3 for x=2 , y= 1
But y+2x is not a multiple of 3 for x=2 and y=1

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