On Z, the set of integers define a relation R as follows a,b∈Z, aRb if 3∣(2a+b) then

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

R is reflexive, symmetric but not transitive

R is reflexive, transitive but not symmetric

R is anti-symmetric

R is an equivalence relation

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

If a∈Z,aRa as3∣(2a+a)R is reflexive.Suppose a R b ⇒ 3∣(2a+b) ⇒ 3∣(3a+b−a) ⇒ 3|(b−a) ⇒3|(a−b) ⇒ 3|(3b+a−b)⇒3|(2b+a) ⇒ b~a. ⇒ Ris symmetric.Next, suppose a R b, b R c ⇒3|(2a+b),3|(2b+c)⇒3|(b−a),3|(c−b)⇒3∣(b−a+c−b)⇒3∣(c−a)⇒3∣(c−a+3a)⇒3∣(2a+c)∴aRcR is transitive. Hence, R is an equivalence relation

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th