JEE Mains · Maths · STD 12 - 1. relation and function
The relation \(R =\{( a , b ): \operatorname{gcd}( a , b )=1,2 a \neq b , a , b \in Z \}\) is:
- A transitive but not reflexive
- B symmetric but not transitive
- C reflexive but not symmetric
- D neither symmetric nor transitive
Answer & Solution
Correct Answer
(D) neither symmetric nor transitive
Step-by-step Solution
Detailed explanation
Reflexive : \((a, a) \Rightarrow \operatorname{gcd}\) of \((a, a)=1\) Which is not true for every a \(\epsilon Z\). Symmetric: Take \(a =2, b =1 \Rightarrow \operatorname{gcd}(2,1)=1\) Also \(2 a=4 \neq b\) Now when \(a =1, b =2 \Rightarrow \operatorname{gcd}(1,2)=1\) Also now…
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