A) reflexive, but not symmetric
B) symmetric only
C) reflexive and transitive
D) reflexive, symmetric and transitive
E) not reflexive, not symmetric and not transitive
Correct Answer: B
Solution :
The relation R is defined by\[aRb,\]if and only if the GCD of a and b is 2. (i)\[oRa,\]then GCD of a and a is a. \[\therefore \]R is not reflexive (ii) \[aRb\Rightarrow bRa\] If GCD of a and b is 2, then GCD of b and a is 2. \[\therefore \] R is symmetric (iii) \[aRb,\text{ }bRc\Rightarrow cRa\] If GCD of a and b is 2 and GCD of b and c is 2, then it is need not to be GCD of c and a is 2. \[\therefore \]R is not transitive.
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