question_answer

Let p be the relation on the set R of all real numbers defined by \[{{a}_{p}}b\] if \[|a-b|\,\,\le \frac{1}{2},\] then p is ______.

A)  reflexive and symmetric but not transitive

B)  transitive but neither reflexive nor symmetric

C)  symmetric and transitive but not reflexive

D)  transitive and reflexive but not symmetric

E)  None of these