jee-main 2023 Q67

jee-main · India · session1_24jan_shift1 Proof True/False Justification
The relation $R = a , b : \operatorname { gcd} a , b = 1 , \quad 2 a \neq b , \quad a , \quad b \in \mathbb { Z }$ is:
(1) transitive but not reflexive
(2) symmetric but not transitive
(3) reflexive but not symmetric
(4) neither symmetric nor transitive
The relation $R = a , b : \operatorname { gcd} a , b = 1 , \quad 2 a \neq b , \quad a , \quad b \in \mathbb { Z }$ is:\\
(1) transitive but not reflexive\\
(2) symmetric but not transitive\\
(3) reflexive but not symmetric\\
(4) neither symmetric nor transitive