A) Reflexive, but not symmetric
B) Symmetric only
C) Reflexive and transitive
D) Not reflexive, not symmetric, not transitive
Correct Answer: B
Solution :
| \[\operatorname{a} R a\], then GCD of a and a is a. |
| \[\therefore \]R is not reflexive. |
| Now, \[\operatorname{aRb}\Rightarrow bRa\] |
| If GCD of a and b is 2, then GCD of band a is 2. |
| \[\therefore \]R is symmetric. |
| Now. \[\operatorname{aRb},bRc\,aRc\] |
| If GCD of a and b is 2 and GCD of b and c is |
| 2, then it need not be GCD of a and c is |
| 2. \[\therefore \]R is not transitive. |
| e.g.,\[6\operatorname{R}2,2\operatorname{R}12\operatorname{but}\text{ }612.\] |
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